Hidden Bibliographic Details
| ISBN: | 9789811618963
9811618968
981161895X
9789811618956
9789811618970
9811618976
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| Digital file characteristics: | text file PDF
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| Notes: | Includes bibliographical references and indexes.
Description based on online resource; title from digital title page (viewed on June 17, 2021).
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| Summary: | The classical ojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the ojasiewiczSimon 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 ojasiewiczSimon gradient inequality. In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual ojasiewiczSimon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reactiondiffusion equations with discontinuous coefficients, reactiondiffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the KellerSegel equations even for higher-dimensional ones.
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| Other form: | Print version: Yagi, Atsushi Abstract Parabolic Evolution Equations and Łojasiewicz-Simon Inequality I Singapore : Springer Singapore Pte. Limited,c2021 9789811618956
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| Standard no.: | 10.1007/978-981-16-1896-3
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