Banasiak, J.
Overview
Works:  18 works in 106 publications in 2 languages and 2,551 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA182, 512.27 
Publication Timeline
.
Most widely held works by
J Banasiak
Perturbations of positive semigroups with applications by
J Banasiak(
Book
)
24 editions published between 2005 and 2006 in English and held by 187 WorldCat member libraries worldwide
"Perturbations of Positive Semigroups with Applications is a selfcontained introduction to semigroup theory with emphasis on positive semigroups on Banach lattices and perturbation techniques. The first part of the book, which should be regarded as an extended reference section, presents a survey of the results from functional analysis, the theory of positive operators and the theory of semigroups that are needed for the second, applied part of the book; worked examples are provided to help absorb the theoretical material
24 editions published between 2005 and 2006 in English and held by 187 WorldCat member libraries worldwide
"Perturbations of Positive Semigroups with Applications is a selfcontained introduction to semigroup theory with emphasis on positive semigroups on Banach lattices and perturbation techniques. The first part of the book, which should be regarded as an extended reference section, presents a survey of the results from functional analysis, the theory of positive operators and the theory of semigroups that are needed for the second, applied part of the book; worked examples are provided to help absorb the theoretical material
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 180 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 180 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
Singularly perturbed evolution equations with applications to kinetic theory by
J. R Mika(
Book
)
7 editions published in 1995 in English and held by 101 WorldCat member libraries worldwide
In recent years there appeared a large number of papers as well as chapters in more general monographs devoted to evolution equations containing small (or large) parameters. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph
7 editions published in 1995 in English and held by 101 WorldCat member libraries worldwide
In recent years there appeared a large number of papers as well as chapters in more general monographs devoted to evolution equations containing small (or large) parameters. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph
Evolutionary equations with applications in natural sciences by
J Banasiak(
Book
)
14 editions published between 2014 and 2015 in English and held by 97 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
14 editions published between 2014 and 2015 in English and held by 97 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
Mathematical modelling in one dimension : an introduction via difference and differential equations by
J Banasiak(
Book
)
12 editions published in 2013 in English and Undetermined and held by 77 WorldCat member libraries worldwide
Difference and Differential Equations in Mathematical Modelling 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
12 editions published in 2013 in English and Undetermined and held by 77 WorldCat member libraries worldwide
Difference and Differential Equations in Mathematical Modelling 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
Methods of small parameter in mathematical biology by
J Banasiak(
Book
)
10 editions published in 2014 in English and held by 22 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
10 editions published in 2014 in English and held by 22 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
)
6 editions published in 2015 in English and held by 8 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 oper
6 editions published in 2015 in English and held by 8 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 oper
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
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
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
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
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
Mathematical modelling in one dimension an introduction via difference and differential equations by
J Banasiak(
)
in English and held by 1 WorldCat member library worldwide
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
Singularly Perturbed Evolution Equations with Applications to Kinetic Theory by
J. R Mika(
)
2 editions published in 1995 in English and held by 0 WorldCat member libraries worldwide
In recent years there appeared a large number of papers as well as chapters in more general monographs devoted to evolution equations containing small (or large) parameters. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph
2 editions published in 1995 in English and held by 0 WorldCat member libraries worldwide
In recent years there appeared a large number of papers as well as chapters in more general monographs devoted to evolution equations containing small (or large) parameters. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph
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BiologyMathematical models Biomathematics Difference equations Differentiable dynamical systems Differential equations Differential equations, Nonlinear Differential equations, Partial Distribution (Probability theory) Engineering mathematics Epidemiology Evolutionary computation Evolution equations Functional analysis GeneticsMathematics 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) Scaling laws (Statistical physics) Semigroups Semigroups of operators Stochastic processes