Abstract Parabolic Evolution Equations and Lojasiewicz-simon Inequality: Abstract Theory - Brossura

Yagi, Atsushi

Brossura

ISBN 10: 981161895X ISBN 13: 9789811618956

Casa editrice: Springer Nature, 2021

Riassunto

The classical Lojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Lojasiewicz–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 Lojasiewicz–Simon gradient inequality.

In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Lojasiewicz–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.

Dettagli dell'edizione

• Editore: Springer Nature
• Data di pubblicazione: 2021
• Lingua: Inglese
• ISBN 10: 981161895X
• ISBN 13: 9789811618956
• Rilegatura: Copertina flessibile
• Numero edizione: 1
• Numero di pagine: 61
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania