Abstract Parabolic Evolution Equations and their Applications

Abstract Parabolic Evolution Equations and their Applications
Author: Atsushi Yagi
Publisher: Springer Science & Business Media
Total Pages: 594
Release: 2009-11-03
Genre: Mathematics
ISBN: 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


Abstract Parabolic Evolution Equations and their Applications
Language: en
Pages: 594
Authors: Atsushi Yagi
Categories: Mathematics
Type: BOOK - Published: 2009-11-03 - Publisher: Springer Science & Business Media

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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
Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality II
Language: en
Pages: 128
Authors: Atsushi Yagi
Categories: Mathematics
Type: BOOK - Published: 2021-08-12 - Publisher: Springer Nature

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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 a
Abstract Parabolic Evolution Equations and Łojasiewicz-Simon Inequality II
Language: en
Pages: 0
Authors: Atsushi Yagi
Categories:
Type: BOOK - Published: 2021 - Publisher:

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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 a
Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I
Language: en
Pages: 68
Authors: Atsushi Yagi
Categories: Mathematics
Type: BOOK - Published: 2021-05-31 - Publisher: Springer Nature

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The classical Łojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Łojasiewicz–Simon grad
Nonlocal and Abstract Parabolic Equations and Their Applications
Language: en
Pages: 332
Authors: Piotr Mucha
Categories: Differential equations, Parabolic
Type: BOOK - Published: 2009 - Publisher:

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