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- W33011689 abstract "This chapter highlights the facts about nonlinear semigroups in arbitrary Banach spaces and an exposition of some applications and extensions of this general theory to certain nonlinear partial differential equations of parabolic type. The chapter focuses on the applicability of the abstract considerations to several concrete problems, to explain what useful information semigroup theory provides and what it does not, and to demonstrate how in certain cases, various partial differential equations techniques can be used to extend the theoretical understanding. The chapter presents the basic working information about nonlinear semigroups, including Crandall–Liggett generation theorem and various regularity and perturbation results. It also presents the nonlinear Chernoff theorem and several related topics, with a view toward the applications. These are the porous medium and related equations, certain variational and quasi-variational inequalities of evolution, and Bellman's equation." @default.
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- W33011689 date "1978-01-01" @default.
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- W33011689 title "Application of Nonlinear Semigroup Theory to Certain Partial Differential Equations" @default.
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- W33011689 doi "https://doi.org/10.1016/b978-0-12-195250-1.50014-x" @default.
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