Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I: Abstract Theory (SpringerBriefs in Mathematics) - Softcover

Yagi, Atsushi

 
9789811618956: Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I: Abstract Theory (SpringerBriefs in Mathematics)
Softcover
ISBN 10: 981161895X ISBN 13: 9789811618956
Verlag: Springer, 2021

Inhaltsangabe

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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Verlag
Springer
Erscheinungsdatum
2021
Sprache
Englisch
ISBN 10 
981161895X
ISBN 13 
9789811618956
Einband
Taschenbuch
Auflage
1
Anzahl der Seiten
71
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