Pascal Cherrier's Books

Evolution Equations of von Karman Type

By: Pascal Cherrier,Albert Milani

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Evolution Equations of von Karman Type

By: Pascal Cherrier,Albert Milani

In these notes we consider two kinds of nonlinear evolution problems of von Karman type on Euclidean spaces of arbitrary even dimension. Each of these problems consists of a system that results from the coupling of two highly nonlinear partial differential equations, one hyperbolic or parabolic and the other elliptic. These systems take their name from a formal analogy with the von Karman equations in the theory of elasticity in two dimensional space. We establish local (respectively global) results for strong (resp., weak) solutions of these problems and corresponding well-posedness results in the Hadamard sense. Results are found by obtaining regularity estimates on solutions which are limits of a suitable Galerkin approximation scheme. The book is intended as a pedagogical introduction to a number of meaningful application of classical methods in nonlinear Partial Differential Equations of Evolution. The material is self-contained and most proofs are given in full detail. The interested reader will gain a deeper insight into the power of nontrivial a priori estimate methods in the qualitative study of nonlinear differential equations.

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Page Count

155

Publisher

Springer

Published Date

ISBN 10

3319209973

ISBN 13

9783319209975

Linear and Quasi-linear Evolution Equations in Hilbert Spaces

By: Pascal Cherrier,Albert Milani

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Linear and Quasi-linear Evolution Equations in Hilbert Spaces

By: Pascal Cherrier,Albert Milani

This book considers evolution equations of hyperbolic and parabolic type. These equations are studied from a common point of view, using elementary methods, such as that of energy estimates, which prove to be quite versatile. The authors emphasize the Cauchy problem and present a unified theory for the treatment of these equations. In particular, they provide local and global existence results, as well as strong well-posedness and asymptotic behavior results for the Cauchy problem for quasi-linear equations. Solutions of linear equations are constructed explicitly, using the Galerkin method; the linear theory is then applied to quasi-linear equations, by means of a linearization and fixed-point technique. The authors also compare hyperbolic and parabolic problems, both in terms of singular perturbations, on compact time intervals, and asymptotically, in terms of the diffusion phenomenon, with new results on decay estimates for strong solutions of homogeneous quasi-linear equations of each type. This textbook presents a valuable introduction to topics in the theory of evolution equations, suitable for advanced graduate students. The exposition is largely self-contained. The initial chapter reviews the essential material from functional analysis. New ideas are introduced along with their context. Proofs are detailed and carefully presented. The book concludes with a chapter on applications of the theory to Maxwell's equations and von Karman's equations.

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Page Count

400

Publisher

American Mathematical Society

Published Date

ISBN 10

1470471442

ISBN 13

9781470471446

Evolutionary Algorithms for Mobile Ad Hoc Networks

By: Bernabé Dorronsoro,Patricia Ruiz,Grégoire Danoy,Yoann Pigné,Pascal Bouvry

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Evolutionary Algorithms for Mobile Ad Hoc Networks

By: Bernabé Dorronsoro,Patricia Ruiz,Grégoire Danoy,Yoann Pigné,Pascal Bouvry

Describes how evolutionary algorithms (EAs) can be used to identify, model, and minimize day-to-day problems that arise for researchers in optimization and mobile networking Mobile ad hoc networks (MANETs), vehicular networks (VANETs), sensor networks (SNs), and hybrid networks—each of these require a designer’s keen sense and knowledge of evolutionary algorithms in order to help with the common issues that plague professionals involved in optimization and mobile networking. This book introduces readers to both mobile ad hoc networks and evolutionary algorithms, presenting basic concepts as well as detailed descriptions of each. It demonstrates how metaheuristics and evolutionary algorithms (EAs) can be used to help provide low-cost operations in the optimization process—allowing designers to put some “intelligence” or sophistication into the design. It also offers efficient and accurate information on dissemination algorithms, topology management, and mobility models to address challenges in the field. Evolutionary Algorithms for Mobile Ad Hoc Networks: Instructs on how to identify, model, and optimize solutions to problems that arise in daily research Presents complete and up-to-date surveys on topics like network and mobility simulators Provides sample problems along with solutions/descriptions used to solve each, with performance comparisons Covers current, relevant issues in mobile networks, like energy use, broadcasting performance, device mobility, and more Evolutionary Algorithms for Mobile Ad Hoc Networks is an ideal book for researchers and students involved in mobile networks, optimization, advanced search techniques, and multi-objective optimization.

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Page Count

186

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118832027

ISBN 13

9781118832028

Evolution Equations of von Karman Type

By: Pascal Cherrier,Albert Milani

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Evolution Equations of von Karman Type

By: Pascal Cherrier,Albert Milani

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

155

Publisher

Springer

Published Date

ISBN 10

3319209973

ISBN 13

9783319209975

Book's by Pascal Cherrier

Evolution Equations of von Karman Type

Evolution Equations of von Karman Type

Linear and Quasi-linear Evolution Equations in Hilbert Spaces

Linear and Quasi-linear Evolution Equations in Hilbert Spaces

Evolutionary Algorithms for Mobile Ad Hoc Networks

Evolutionary Algorithms for Mobile Ad Hoc Networks

Evolution Equations of von Karman Type

Evolution Equations of von Karman Type

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