期刊全稱 | Abstract Parabolic Evolution Equations and ?ojasiewicz–Simon Inequality I | 期刊簡稱 | Abstract Theory | 影響因子2023 | Atsushi Yagi | 視頻video | http://file.papertrans.cn/144/143464/143464.mp4 | 發(fā)行地址 | Makes an extended version of the Lojasiewicz–Simon inequality more available to certain concrete problems.Offers a unified method to show asymptotic convergence of solutions for nonlinear parabolic eq | 學(xué)科分類 | SpringerBriefs in Mathematics | 圖書封面 |  | 影響因子 | The classical ?ojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the ?ojasiewicz–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 ?ojasiewicz–Simon gradient inequality..In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual ?ojasiewicz–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.. | Pindex | Book 2021 |
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