Jacek Banasiak's Books

Singularly Perturbed Evolution Equations With Applications To Kinetic Theory

By: Jacek Banasiak,Janusz R Mika

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Singularly Perturbed Evolution Equations With Applications To Kinetic Theory

By: Jacek Banasiak,Janusz R Mika

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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Page Count

325

Publisher

World Scientific

Published Date

ISBN 10

9814500976

ISBN 13

9789814500975

Analytic Methods for Coagulation-Fragmentation Models, Volume I

By: Jacek Banasiak,Wilson Lamb,Philippe Laurencot

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Analytic Methods for Coagulation-Fragmentation Models, Volume I

By: Jacek Banasiak,Wilson Lamb,Philippe Laurencot

Analytic Methods for Coagulation-Fragmentation Models is a two-volume set that provides a comprehensive exposition of the mathematical analysis of coagulation-fragmentation models. Initially, an in-depth survey of coagulation-fragmentation processes is presented, together with an account of relevant early results obtained on the associated model equations. These provide motivation for the subsequent detailed treatment of more up-to-date investigations which have led to significant theoretical developments on topics such as solvability and the long-term behaviour of solutions. To make the account as self-contained as possible, the mathematical tools that feature prominently in these modern treatments are introduced at appropriate places. The main theme of Volume I is the analysis of linear fragmentation models, with Volume II devoted to processes that involve the nonlinear contribution of coagulation. Features of Volume I: The main models of the theory together with their derivations and early methods of solution A detailed presentation of the operator theoretical methods and semigroup theory that play an essential role in the theory of fragmentation processes A comprehensive theory of fragmentation processes, including fragmentation with growth and decay in both the discrete and continuous particle size cases An analytical explanation of the `pathologies’ of the fragmentation equation, such as the shattering phase transition and non-uniqueness of solutions An analysis of the long-term dynamics of the discrete size fragmentation equation with growth

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Page Count

354

Publisher

CRC Press

Published Date

ISBN 10

1498772668

ISBN 13

9781498772662

Multiscale Problems in the Life Sciences

From Microscopic to Macroscopic

By: Jacek Banasiak,Jacek Miekisz

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Multiscale Problems in the Life Sciences

From Microscopic to Macroscopic

By: Jacek Banasiak,Jacek Miekisz

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.

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341

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540783601

ISBN 13

9783540783602

From Genetics to Mathematics

By: Miros?aw Lachowicz,Jacek Miekisz

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From Genetics to Mathematics

By: Miros?aw Lachowicz,Jacek Miekisz

This volume contains pedagogical and elementary introductions to genetics for mathematicians and physicists as well as to mathematical models and techniques of population dynamics. It also offers a physicist's perspective on modeling biological processes. Each chapter starts with an overview followed by the recent results obtained by authors. Lectures are self-contained and are devoted to various phenomena such as the evolution of the genetic code and genomes, age-structured populations, demography, sympatric speciation, the Penna model, LotkaVolterra and other predator-prey models, evolutionary models of ecosystems, extinctions of species, and the origin and development of language. Authors analyze their models from the computational and mathematical points of view.

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Page Count

242

Publisher

World Scientific

Published Date

ISBN 10

9812837248

ISBN 13

9789812837240

Methods of Small Parameter in Mathematical Biology

By: Jacek Banasiak,Mirosław Lachowicz

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Methods of Small Parameter in Mathematical Biology

By: Jacek Banasiak,Mirosław Lachowicz

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 to the purpose at hand and preserves the salient features of the dynamics. Many ad hoc methods have been devised, and the aim of this book is to present a systematic way of deriving the so-called 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 the authors describe 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 applied and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis.

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Page Count

295

Publisher

Springer Science & Business

Published Date

ISBN 10

3319051407

ISBN 13

9783319051406

Mathematical Modelling in One Dimension

An Introduction via Difference and Differential Equations

By: Jacek Banasiak

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Mathematical Modelling in One Dimension

An Introduction via Difference and Differential Equations

By: Jacek Banasiak

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 self-guided 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.

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Page Count

121

Publisher

Cambridge University Press

Published Date

ISBN 10

1107311519

ISBN 13

9781107311510

Multiscale Problems in the Life Sciences

From Microscopic to Macroscopic

By: Jacek Banasiak,Vincenzo Capasso,Miroslaw Lachowicz,Jacek Miekisz

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Multiscale Problems in the Life Sciences

From Microscopic to Macroscopic

By: Jacek Banasiak,Vincenzo Capasso,Miroslaw Lachowicz,Jacek Miekisz

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Page Count

340

Publisher

Springer

Published Date

ISBN 10

3540783628

ISBN 13

9783540783626

Analytic Methods for Coagulation-Fragmentation Models, Volume I

By: Jacek Banasiak,Wilson Lamb,Philippe Laurencot

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Analytic Methods for Coagulation-Fragmentation Models, Volume I

By: Jacek Banasiak,Wilson Lamb,Philippe Laurencot

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Page Count

330

Publisher

CRC Press

Published Date

ISBN 10

1351650467

ISBN 13

9781351650465

Perturbations of Positive Semigroups with Applications

By: Jacek Banasiak,Luisa Arlotti

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Perturbations of Positive Semigroups with Applications

By: Jacek Banasiak,Luisa Arlotti

This book deals mainly with modelling systems that change with time. The evolution equations that it describes can be found in a number of application areas, such as kinetics, fragmentation theory and mathematical biology. This will be the first self-contained account of the area.

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Page Count

438

Publisher

Springer

Published Date

ISBN 10

1848008902

ISBN 13

9781848008908

Perturbations of Positive Semigroups with Applications

By: Jacek Banasiak,Luisa Arlotti

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Perturbations of Positive Semigroups with Applications

By: Jacek Banasiak,Luisa Arlotti

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443

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1846281539

ISBN 13

9781846281532

Analytic Methods for Coagulation-Fragmentation Models

By: Jacek Banasiak,Wilson Lamb,Philippe Laurencot

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Analytic Methods for Coagulation-Fragmentation Models

By: Jacek Banasiak,Wilson Lamb,Philippe Laurencot

Analytic Methods for Coagulation-Fragmentation Models is a two-volume set that provides a comprehensive exposition of the mathematical analysis of coagulation-fragmentation models. Initially, an in-depth survey of coagulation-fragmentation processes is presented, together with an account of relevant early results obtained on the associated model equations. These provide motivation for the subsequent detailed treatment of more up-to-date investigations which have led to significant theoretical developments on topics such as solvability and the long-term behaviour of solutions. To make the account as self-contained as possible, the mathematical tools that feature prominently in these modern treatments are introduced at appropriate places. The main theme of Volume I is the analysis of linear fragmentation models, with Volume II devoted to processes that involve the nonlinear contribution of coagulation. Features of Volume I: The main models of the theory together with their derivations and early methods of solution A detailed presentation of the operator theoretical methods and semigroup theory that play an essential role in the theory of fragmentation processes A comprehensive theory of fragmentation processes, including fragmentation with growth and decay in both the discrete and continuous particle size cases An analytical explanation of the `pathologies' of the fragmentation equation, such as the shattering phase transition and non-uniqueness of solutions An analysis of the long-term dynamics of the discrete size fragmentation equation with growth

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Page Count

354

Publisher

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Published Date

ISBN 10

149877265X

ISBN 13

9781498772655

Book's by Jacek Banasiak

Singularly Perturbed Evolution Equations With Applications To Kinetic Theory

Singularly Perturbed Evolution Equations With Applications To Kinetic Theory

Analytic Methods for Coagulation-Fragmentation Models, Volume I

Analytic Methods for Coagulation-Fragmentation Models, Volume I

Multiscale Problems in the Life Sciences

Multiscale Problems in the Life Sciences

From Genetics to Mathematics

From Genetics to Mathematics

Methods of Small Parameter in Mathematical Biology

Methods of Small Parameter in Mathematical Biology

Mathematical Modelling in One Dimension

Mathematical Modelling in One Dimension

Multiscale Problems in the Life Sciences

Multiscale Problems in the Life Sciences

Analytic Methods for Coagulation-Fragmentation Models, Volume I

Analytic Methods for Coagulation-Fragmentation Models, Volume I

Perturbations of Positive Semigroups with Applications

Perturbations of Positive Semigroups with Applications

Perturbations of Positive Semigroups with Applications

Perturbations of Positive Semigroups with Applications

Analytic Methods for Coagulation-Fragmentation Models

Analytic Methods for Coagulation-Fragmentation Models

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