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Abstract Parabolic Evolution Equations and Lojasiewicz–Simon Inequality I

- Abstract Theory
Af: Atsushi Yagi Engelsk Paperback

Abstract Parabolic Evolution Equations and Lojasiewicz–Simon Inequality I

- Abstract Theory
Af: Atsushi Yagi Engelsk Paperback
Tjek vores konkurrenters priser
The classical Łojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Łojasiewicz-Simon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this Łojasiewicz-Simon gradient inequality.

In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Łojasiewicz-Simon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reaction-diffusion equations with discontinuous coefficients, reaction-diffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the Keller-Segel equations even for higher-dimensional ones.

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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 gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this Łojasiewicz-Simon gradient inequality.

In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Łojasiewicz-Simon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reaction-diffusion equations with discontinuous coefficients, reaction-diffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the Keller-Segel equations even for higher-dimensional ones.

Produktdetaljer
Sprog: Engelsk
Sider: 61
ISBN-13: 9789811618956
Indbinding: Paperback
Udgave:
ISBN-10: 981161895X
Udg. Dato: 1 jun 2021
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Verlag, Singapore
Oplagsdato: 1 jun 2021
Forfatter(e): Atsushi Yagi
Forfatter(e) Atsushi Yagi


Kategori Funktionsanalyse og transformation


ISBN-13 9789811618956


Sprog Engelsk


Indbinding Paperback


Sider 61


Udgave


Længde 0mm


Bredde 155mm


Højde 235mm


Udg. Dato 1 jun 2021


Oplagsdato 1 jun 2021


Forlag Springer Verlag, Singapore

Kategori sammenhænge