Banasiak, J.
Overview
Works:  18 works in 116 publications in 2 languages and 2,747 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Publication Timeline
.
Most widely held works by
J Banasiak
Perturbations of positive semigroups with applications by
J Banasiak(
Book
)
26 editions published between 2005 and 2006 in English and held by 206 WorldCat member libraries worldwide
The second part then deals with the application of the developed theory to a variety of problems ranging from the classical birthanddeath type problems of population dynamics, through fragmentation models in both conservative and mass loss regimes, to kinetic models."Jacket
26 editions published between 2005 and 2006 in English and held by 206 WorldCat member libraries worldwide
The second part then deals with the application of the developed theory to a variety of problems ranging from the classical birthanddeath type problems of population dynamics, through fragmentation models in both conservative and mass loss regimes, to kinetic models."Jacket
Multiscale problems in the life sciences : from microscopic to macroscopic : lectures given at the Banach Center and C.I.M.E.
joint summer school held in Będlewo, Poland, September 49, 2006 by
J Banasiak(
Book
)
21 editions published in 2008 in English and held by 176 WorldCat member libraries worldwide
The aim of this volume that presents Lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to Biology and Medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory and game theory
21 editions published in 2008 in English and held by 176 WorldCat member libraries worldwide
The aim of this volume that presents Lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to Biology and Medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory and game theory
Evolutionary equations with applications in natural sciences by
J Banasiak(
Book
)
13 editions published between 2014 and 2015 in English and held by 110 WorldCat member libraries worldwide
With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. The unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering
13 editions published between 2014 and 2015 in English and held by 110 WorldCat member libraries worldwide
With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. The unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering
Singularly perturbed evolution equations with applications to kinetic theory by
J. R Mika(
Book
)
10 editions published in 1995 in English and held by 107 WorldCat member libraries worldwide
1. Introduction  2. Mathematical preliminaries. 1. Introduction. 2. General definitions and notation. 3. Banach and Hilbert spaces. 4. Distributions and Sobolev spaces. 5. Vectorvalued functions. 6. Unbounded operators. 7. Elements of spectral theory  3. Semigroup theory. 1. Introduction. 2. Generation of semigroups. 3. Fractional powers of closed operators. 4. Perturbation theorems. 5. Asymptotic behaviour of solutions. 6. Inhomogeneous Cauchy problem. 7. Applications to partial differential equations  4. Development of asymptotic methods for singularly perturbed evolution equations. 1. Introduction. 2. Single evolution equations with a small parameter. 3. Systems of evolution equations with a small parameter  5. Some singularsingularly perturbed evolution equations and kinetic equation. 1. Singularsingularly perturbed evolution equations. 2. Model system: exact solution. 3. Model system: standard asymptotic analysis. 4. Model system: compressed asymptotic expansion. 5. Modified model system. 6. Singularsingularly perturbed evolution equations: compressed approach. 7. Singularly perturbed linear kinetic equations  6. Hilbert space theory for equations of kinetic type. 1. Introduction. 2. Preliminary results. 3. Properties of terms of expansion. 4. Estimates of error of asymptotic expansion. 5. Remarks on nonselfadjointness of C  7. Applications to kinetic equations with bounded collision operators. 1. Introduction. 2. Properties of linear Boltzmann equation with unbounded velocity range. 3. Diffusion approximation to linear Boltzmann equation  8. Applications to equations of FokkerPlanck type. 1. Introduction. 2. General assumptions. 3. Variational setting. 4. FokkerPlanck equation of electron scattering in plasma. 5. FokkerPlanck equation of Brownian motion. 6. FokkerPlanck equation of vibrational relaxation of harmonic oscillator  9. Applications to spatially inhomogeneous linear Boltzmann equation. 1. Introduction. 2. Properties of neutron transport equation in slab geometry. 3. Asymptotic expansion. 4. Remarks on general spatially inhomogeneous equation  10. Application to kinetic equation with external field. 1. Introduction. 2. Properties of collision operator. 3. Formal asymptotic formulae. 4. Initial layer part. 5. Bulk part. 6. Error of asymptotic expansion  11. Miscellaneous results. 1. Introduction. 2. Asymptotic analysis of telegraph systems. 3. Remarks on compressed asymptotic method in L[symbol]setting. 4. Carleman model
10 editions published in 1995 in English and held by 107 WorldCat member libraries worldwide
1. Introduction  2. Mathematical preliminaries. 1. Introduction. 2. General definitions and notation. 3. Banach and Hilbert spaces. 4. Distributions and Sobolev spaces. 5. Vectorvalued functions. 6. Unbounded operators. 7. Elements of spectral theory  3. Semigroup theory. 1. Introduction. 2. Generation of semigroups. 3. Fractional powers of closed operators. 4. Perturbation theorems. 5. Asymptotic behaviour of solutions. 6. Inhomogeneous Cauchy problem. 7. Applications to partial differential equations  4. Development of asymptotic methods for singularly perturbed evolution equations. 1. Introduction. 2. Single evolution equations with a small parameter. 3. Systems of evolution equations with a small parameter  5. Some singularsingularly perturbed evolution equations and kinetic equation. 1. Singularsingularly perturbed evolution equations. 2. Model system: exact solution. 3. Model system: standard asymptotic analysis. 4. Model system: compressed asymptotic expansion. 5. Modified model system. 6. Singularsingularly perturbed evolution equations: compressed approach. 7. Singularly perturbed linear kinetic equations  6. Hilbert space theory for equations of kinetic type. 1. Introduction. 2. Preliminary results. 3. Properties of terms of expansion. 4. Estimates of error of asymptotic expansion. 5. Remarks on nonselfadjointness of C  7. Applications to kinetic equations with bounded collision operators. 1. Introduction. 2. Properties of linear Boltzmann equation with unbounded velocity range. 3. Diffusion approximation to linear Boltzmann equation  8. Applications to equations of FokkerPlanck type. 1. Introduction. 2. General assumptions. 3. Variational setting. 4. FokkerPlanck equation of electron scattering in plasma. 5. FokkerPlanck equation of Brownian motion. 6. FokkerPlanck equation of vibrational relaxation of harmonic oscillator  9. Applications to spatially inhomogeneous linear Boltzmann equation. 1. Introduction. 2. Properties of neutron transport equation in slab geometry. 3. Asymptotic expansion. 4. Remarks on general spatially inhomogeneous equation  10. Application to kinetic equation with external field. 1. Introduction. 2. Properties of collision operator. 3. Formal asymptotic formulae. 4. Initial layer part. 5. Bulk part. 6. Error of asymptotic expansion  11. Miscellaneous results. 1. Introduction. 2. Asymptotic analysis of telegraph systems. 3. Remarks on compressed asymptotic method in L[symbol]setting. 4. Carleman model
Mathematical modelling in one dimension : an introduction via difference and differential equations by
J Banasiak(
Book
)
13 editions published in 2013 in English and Undetermined and held by 89 WorldCat member libraries worldwide
Mathematical Modelling in One Dimension demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a selfguided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, showing how they complement and intertwine in describing natural phenomena
13 editions published in 2013 in English and Undetermined and held by 89 WorldCat member libraries worldwide
Mathematical Modelling in One Dimension demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a selfguided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, showing how they complement and intertwine in describing natural phenomena
Methods of small parameter in mathematical biology by
J Banasiak(
Book
)
13 editions published between 2014 and 2016 in English and held by 26 WorldCat member libraries worldwide
This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant and preserves the salient features of the dynamics. The aim of this book is to present a systematic way of deriving the socalled limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools described allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value. The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques. Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and graduate students in appled and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis
13 editions published between 2014 and 2016 in English and held by 26 WorldCat member libraries worldwide
This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant and preserves the salient features of the dynamics. The aim of this book is to present a systematic way of deriving the socalled limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools described allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value. The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques. Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and graduate students in appled and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis
Semigroups of operators : theory and applications Be̜dlewo, Poland, October 2013 by
J Banasiak(
Book
)
8 editions published between 2015 and 2016 in English and held by 11 WorldCat member libraries worldwide
Many results, both from semigroup theory itself and from the applied sciences, are phrased in disciplinespecific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semigroup theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various subdisciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a welldeveloped branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator theory. Nowadays, it still has the same distinctive flavour: it develops rapidly by posing new ?internal? questions and, in answering them, discovering new methods that can be used in applications. On the other hand, it is influenced by questions from PDEs and stochastic processes as well as from applied sciences such as mathematical biology and optimal control, and thus it continually gathers a new momentum. Researchers and postgraduate students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimization and optimal control will find this volume useful
8 editions published between 2015 and 2016 in English and held by 11 WorldCat member libraries worldwide
Many results, both from semigroup theory itself and from the applied sciences, are phrased in disciplinespecific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semigroup theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various subdisciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a welldeveloped branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator theory. Nowadays, it still has the same distinctive flavour: it develops rapidly by posing new ?internal? questions and, in answering them, discovering new methods that can be used in applications. On the other hand, it is influenced by questions from PDEs and stochastic processes as well as from applied sciences such as mathematical biology and optimal control, and thus it continually gathers a new momentum. Researchers and postgraduate students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimization and optimal control will find this volume useful
Multiscale problems in the life sciences lectures given at the Banach Center and C.I.M.E. Joint Summer School held in Bedlewo,
Poland September 49, 2006 by
J Banasiak(
)
1 edition published in 2008 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 3 WorldCat member libraries worldwide
Rynek butelek z PET by
J Banasiak(
Book
)
1 edition published in 2001 in Polish and held by 2 WorldCat member libraries worldwide
1 edition published in 2001 in Polish and held by 2 WorldCat member libraries worldwide
Wybrane metody matematyczne teorii populacji i ekologii by
J Banasiak(
Book
)
1 edition published in 2011 in Polish and held by 2 WorldCat member libraries worldwide
1 edition published in 2011 in Polish and held by 2 WorldCat member libraries worldwide
Identyfikacja systemów by
Torsten Söderström(
Book
)
1 edition published in 1997 in Polish and held by 2 WorldCat member libraries worldwide
1 edition published in 1997 in Polish and held by 2 WorldCat member libraries worldwide
Multiple Scales Problems in Biomathematics, Mechanics, Physics and Numerics by mechanics, physics and numerics" CIMPAUNESCOSouth Africa School "Multiple scales problems in biomathematics(
Book
)
2 editions published in 2009 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2009 in English and held by 2 WorldCat member libraries worldwide
Evolution equations in applications(
Book
)
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
Chaotyczne liniowe układy dynamiczne : teoria i zastosowania by
J Banasiak(
)
1 edition published in 2005 in Polish and held by 1 WorldCat member library worldwide
1 edition published in 2005 in Polish and held by 1 WorldCat member library worldwide
Solvability of linear kinetic equations with multienergetic inelastic scattering by
J Banasiak(
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
Age structured models of mathematical epidemiology by Rodrigue Yves M'pika Massoukou(
Book
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
Analytic Methods for CoagulationFragmentation Models by
J Banasiak(
)
1 edition published in 2017 in English and held by 0 WorldCat member libraries worldwide
"The book begins with an indepth survey of coagulationfragmentation models, followed by a detailed presentation of relevant earlier results in the field. The mathematical tools necessary for the modern development of the theory as well as essential facts from infinitedimensional dynamical systems, are introduced. The next few chapters are devoted to methods suitable to cases where the process is dominated by fragmentation. The following chapter focuses on weak compactness methods for solving coagulationfragmentation equations. The final chapter deals with the longterm asymptotic behaviour of solutions to coagulation and fragmentation equations."Provided by publisher
1 edition published in 2017 in English and held by 0 WorldCat member libraries worldwide
"The book begins with an indepth survey of coagulationfragmentation models, followed by a detailed presentation of relevant earlier results in the field. The mathematical tools necessary for the modern development of the theory as well as essential facts from infinitedimensional dynamical systems, are introduced. The next few chapters are devoted to methods suitable to cases where the process is dominated by fragmentation. The following chapter focuses on weak compactness methods for solving coagulationfragmentation equations. The final chapter deals with the longterm asymptotic behaviour of solutions to coagulation and fragmentation equations."Provided by publisher
Multiscale problems in the life sciences : from microscopic to macroscopic : lectures given at the Banach Center and C.I.M.E.
joint summer school held in Bȩdlewo, Poland, September 49, 2006(
)
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
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BiologyMathematical models Biomathematics Difference equations Differentiable dynamical systems Differential equations Differential equations, Partial Distribution (Probability theory) Dynamics Engineering mathematics Epidemiology Ergodic theory Evolutionary computation Evolution equations Functional analysis GeneticsMathematics Graph theory Group extensions (Mathematics) Homogenization (Differential equations) Hyperbolic groups Integral equations Kinetic theory of matter Mathematical models Mathematical optimization Mathematical physics Mathematical statisticsData processing Mathematics Numerical analysis Operator theory Perturbation (Mathematics) Probabilities Scaling laws (Statistical physics) Semigroups Semigroups of operators Stochastic processes