Banasiak, J.
Overview
Works:  10 works in 53 publications in 2 languages and 1,699 library holdings 

Genres:  Conference 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(
)
8 editions published between 2005 and 2006 in English and held by 675 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
8 editions published between 2005 and 2006 in English and held by 675 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 Lectures given at the Banach center and C.I.M.E. joint summer school(
)
13 editions published in 2008 in English and held by 479 WorldCat member libraries worldwide
13 editions published in 2008 in English and held by 479 WorldCat member libraries worldwide
Methods of small parameter in mathematical biology
by
J Banasiak(
)
6 editions published in 2014 in English and held by 227 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
6 editions published in 2014 in English and held by 227 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
Mathematical modelling in one dimension an introduction via difference and differential equations
by
J Banasiak(
)
10 editions published in 2013 in English and held by 176 WorldCat member libraries worldwide
Uses a wide variety of applications to demonstrate the universality of mathematical techniques in describing and analysing natural phenomena
10 editions published in 2013 in English and held by 176 WorldCat member libraries worldwide
Uses a wide variety of applications to demonstrate the universality of mathematical techniques in describing and analysing natural phenomena
Singularly perturbed evolution equations with applications to kinetic theory
by
J. R Mika(
Book
)
7 editions published in 1995 in English and held by 116 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 116 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 CIMPAUNESCOSouth Africa School Evolutionary Equations with Applications in Natural Sciences(
Book
)
3 editions published between 2014 and 2015 in English and held by 18 WorldCat member libraries worldwide
3 editions published between 2014 and 2015 in English and held by 18 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
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
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
Semigroup of operators, theory and applications : Bdlewo, Poland, October 2013
(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
Audience Level
0 

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Related Identities
 Lachowicz, Mirosław Editor
 Arlotti, Luisa
 Capasso, Vincenzo 1945 Editor
 Stefan Banach International Mathematical Center
 Mika, J. R. Author
 MokhtarKharroubi, M. Editor
 Mie̜dzynarodowe Centrum Matematyczne Imienia Stefana Banacha <Warszawa>
 SpringerLink (Service en ligne)
 Centro internazionale matematico estivo
 Abdulle, Assyr
Associated Subjects
BiologyMathematical models Biomathematics Difference equations Differential equations Differential equations, Nonlinear Engineering mathematics Evolution equations Functional analysis GeneticsMathematics Kinetic theory of matter Mathematical models Mathematical optimization Mathematical physics Mathematical statisticsData processing Mathematics Multiscale modeling Numerical analysis Perturbation (Mathematics) Semigroups Stochastic processes