| Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality I: Abstract Theory 2021 Edition Contributor(s): Yagi, Atsushi (Author) |
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ISBN: 981161895X ISBN-13: 9789811618956 Publisher: Springer OUR PRICE: $66.49 Product Type: Paperback - Other Formats Published: June 2021 |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Mathematics | Functional Analysis - Mathematics | Mathematical Analysis |
| Physical Information: 0.15" H x 6.14" W x 9.21" (0.25 lbs) 61 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |