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＜電子ブック＞
Beyond Partial Differential Equations : On Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations / by Horst Reinhard Beyer
(Lecture Notes in Mathematics. ISSN:16179692 ; 1898)

版	1st ed. 2007.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2007
本文言語	英語
大きさ	XIV, 283 p : online resource
著者標目	*Beyer, Horst Reinhard author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Operator theory LCSH:Differential equations FREE:Analysis FREE:Operator Theory FREE:Differential Equations
一般注記	Conventions -- Mathematical Introduction -- Prerequisites -- Strongly Continuous Semigroups -- Examples of Generators of Strongly Continuous Semigroups -- Intertwining Relations, Operator Homomorphisms -- Examples of Constrained Systems -- Kernels, Chains, and Evolution Operators -- The Linear Evolution Equation -- Examples of Linear Evolution Equations -- The Quasi-Linear Evolution Equation -- Examples of Quasi-Linear Evolution Equations The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis. Only some examples require more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Particular stress is on equations of the hyperbolic type since considerably less often treated in the literature. Also, evolution equations from fundamental physics need to be compatible with the theory of special relativity and therefore are of hyperbolic type. Throughout, detailed applications are given to hyperbolic partial differential equations occurring in problems of current theoretical physics, in particular to Hermitian hyperbolic systems. This volume is thus also of interest to readers from theoretical physics HTTP:URL=https://doi.org/10.1007/978-3-540-71129-2

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