Philippe Laurencot's Books

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

Superlinear Parabolic Problems

Blow-up, Global Existence and Steady States

By: Pavol Quittner,Philippe Souplet

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Superlinear Parabolic Problems

Blow-up, Global Existence and Steady States

By: Pavol Quittner,Philippe Souplet

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593

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764384425

ISBN 13

9783764384425

Superlinear Parabolic Problems

Blow-up, Global Existence and Steady States

By: Prof. Dr. Pavol Quittner,Prof. Dr. Philippe Souplet

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Superlinear Parabolic Problems

Blow-up, Global Existence and Steady States

By: Prof. Dr. Pavol Quittner,Prof. Dr. Philippe Souplet

This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.

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Page Count

738

Publisher

Springer

Published Date

ISBN 10

3030182223

ISBN 13

9783030182229

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

Analytic Methods for Coagulation-Fragmentation Models, Volume II

By: Jacek Banasiak,Wilson Lamb,Philippe Laurencot

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Analytic Methods for Coagulation-Fragmentation Models, Volume II

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 II: A primer on weak compactness in L 1 and dynamical systems A comprehensive theory of solvability of the coagulation-fragmentation equation by both the semigroup and weak compactness methods, including a thorough analysis of the gelation and shattering phenomena A detailed analysis of the long-term dynamics of the coagulation-fragmentation equations with a state-of-the-art discussion on self-similar solutions

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Page Count

308

Publisher

CRC Press

Published Date

ISBN 10

1000008150

ISBN 13

9781000008159

Book's by Philippe Laurencot

Analytic Methods for Coagulation-Fragmentation Models, Volume I

Analytic Methods for Coagulation-Fragmentation Models, Volume I

Superlinear Parabolic Problems

Superlinear Parabolic Problems

Superlinear Parabolic Problems

Superlinear Parabolic Problems

Analytic Methods for Coagulation-Fragmentation Models, Volume I

Analytic Methods for Coagulation-Fragmentation Models, Volume I

Analytic Methods for Coagulation-Fragmentation Models, Volume II

Analytic Methods for Coagulation-Fragmentation Models, Volume II

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