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Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I: Abstract Theory (SpringerBriefs in Mathematics) - Softcover
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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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Abstract Parabolic Evolution Equations and ojasiewiczSimon Inequality I (Paperback)
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Springer Verlag, Singapore, Singapore, 2021
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ISBN 13: 9789811618956
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Paperback. Condition: new. Paperback. The classical Lojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the LojasiewiczSimon 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 LojasiewiczSimon gradient inequality.In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual LojasiewiczSimon 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9789811618956
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