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＜電子ブック＞
Evolution Equations of von Karman Type / by Pascal Cherrier, Albert Milani
(Lecture Notes of the Unione Matematica Italiana. ISSN:18629121 ; 17)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
本文言語	英語
大きさ	XVI, 140 p : online resource
著者標目	*Cherrier, Pascal author Milani, Albert author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical physics LCSH:Geometry, Differential FREE:Differential Equations FREE:Mathematical Methods in Physics FREE:Differential Geometry
一般注記	Operators and Spaces -- Weak Solutions --  Strong Solutions, m + k _ 4 -- Semi-Strong Solutions, m = 2, k = 1 In these notes we consider two kinds of nonlinear evolution problems of von Karman type on Euclidean spaces of arbitrary even dimension. Each of these problems consists of a system that results from the coupling of two highly nonlinear partial differential equations, one hyperbolic or parabolic and the other elliptic. These systems take their name from a formal analogy with the von Karman equations in the theory of elasticity in two dimensional space. We establish local (respectively global) results for strong (resp., weak) solutions of these problems and corresponding well-posedness results in the Hadamard sense. Results are found by obtaining regularity estimates on solutions which are limits of a suitable Galerkin approximation scheme. The book is intended as a pedagogical introduction to a number of meaningful application of classical methods in nonlinear Partial Differential Equations of Evolution. The material is self-contained and most proofs are given in full detail. The interested reader will gain a deeper insight into the power of nontrivial a priori estimate methods in the qualitative study of nonlinear differential equations HTTP:URL=https://doi.org/10.1007/978-3-319-20997-5

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