Semilinear Evolution Equations and Their Applications
Semilinear Evolution Equations and Their Applications

Author: Toka Diagana

Publisher: Springer

Published: 2018-10-23

Total Pages: 199

ISBN-13: 303000449X

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This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including degenerate ones. Various stability, uniqueness, and existence results are established using various tools from nonlinear functional analysis and operator theory (such as semigroup methods). Various applications to partial differential equations and the dynamic of populations are amply discussed. This self-contained volume is primarily intended for advanced undergraduate and graduate students, post-graduates and researchers, but may also be of interest to non-mathematicians such as physicists and theoretically oriented engineers. It can also be used as a graduate text on evolution equations and difference equations and their applications to partial differential equations and practical problems arising in population dynamics. For completeness, detailed preliminary background on Banach and Hilbert spaces, operator theory, semigroups of operators, and almost periodic functions and their spectral theory are included as well.

An Introduction to Semilinear Evolution Equations
An Introduction to Semilinear Evolution Equations

Author: Thierry Cazenave

Publisher: Oxford University Press

Published: 1998

Total Pages: 204

ISBN-13: 9780198502777

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This book presents in a self-contained form the typical basic properties of solutions to semilinear evolutionary partial differential equations, with special emphasis on global properties. It has a didactic ambition and will be useful for an applied readership as well as theoretical researchers.

Abstract Parabolic Evolution Equations and their Applications
Abstract Parabolic Evolution Equations and their Applications

Author: Atsushi Yagi

Publisher: Springer Science & Business Media

Published: 2009-11-03

Total Pages: 594

ISBN-13: 3642046312

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This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0

Evolution Equations and Approximations
Evolution Equations and Approximations

Author: Kazufumi Ito

Publisher: World Scientific

Published: 2002

Total Pages: 524

ISBN-13: 9789812380265

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Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR

Evolution Equations and Their Applications in Physical and Life Sciences
Evolution Equations and Their Applications in Physical and Life Sciences

Author: G Lumer

Publisher: CRC Press

Published: 2019-04-24

Total Pages: 532

ISBN-13: 1482277484

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This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physica

Abstract Evolution Equations, Periodic Problems and Applications
Abstract Evolution Equations, Periodic Problems and Applications

Author: D Daners

Publisher: Chapman and Hall/CRC

Published: 1992-12-29

Total Pages: 268

ISBN-13:

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Part of the Pitman Research Notes in Mathematics series, this text covers: linear evolution equations of parabolic type; semilinear evolution equations of parabolic type; evolution equations and positivity; semilinear periodic evolution equations; and applications.

Evolution Equations and Applications
Evolution Equations and Applications

Author: Patrice Ndambomve

Publisher: LAP Lambert Academic Publishing

Published: 2012-07

Total Pages: 100

ISBN-13: 9783659187650

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In this book, we present the fundamental theory of abstract Evolution Equations by using the semigroup approach. More precisely, first we review the basic notions of Functional Analysis and Differential Analysis, secondly we study the theory of semigroups of bounded linear operators, and thirdly we consider Linear Evolution Equations and moreover we give existence results for Semilinear Evolution Equations of the form: du/dt= Au + f(t; u); t 0; u(0) = u_0 where A is a linear operator that is the infinitesimal generator of a C_0-semigroup of bounded linear operators on a Banach space and f satisfies certain Lipschitz, and Linear growth conditions. As applications we show the existence of solutions to some Homogeneous Heat Equations, classical Wave equations, nonlinear Heat Equation, and to some nonlinear Wave equation.

Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality II
Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality II

Author: Atsushi Yagi

Publisher: Springer Nature

Published: 2021-08-12

Total Pages: 128

ISBN-13: 9811626634

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This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described. Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller–Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more. Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed.