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|All Authors / Contributors:||
Pascal Cherrier; A Milani
|Description:||xviii, 377 pages ; 25 cm.|
|Contents:||Functional framework --
Linear equations --
Quasi-linear equations --
Global existence --
Asymptotic behavior --
Singular convergence --
Maxwell and von Karman equations.
|Series Title:||Graduate studies in mathematics, v. 135.|
|Other Titles:||Linear and quasilinear evolution equations in Hilbert spaces|
|Responsibility:||Pascal Cherrier, Albert Milani.|
"This book considers evolution equations of hyperbolic and parabolic type. These equations are studied from a common point of view, using elementary methods, such as that of energy estimates, which prove to be quite versatile. The authors emphasize the Cauchy problem and present More...a unified theory for the treatment of these equations. In particular, they provide local and global existence results, as well as strong well-posedness and asymptotic behavior results for the Cauchy problem for quasi-linear equations. Solutions of linear equations are constructed explicitly, using the Galerkin method; the linear theory is then applied to quasi-linear equations, by means of a linearization and fixed-point technique. The authors also compare hyperbolic and parabolic problems, both in terms of singular perturbations, on compact time intervals, and asymptotically, in terms of the diffusion phenomenon, with new results on decay estimates for strong solutions of homogeneous quasi-linear equations of each type. This textbook presents a valuable introduction to topics in the theory of evolution equations, suitable for advanced graduate students. The exposition is largely self-contained. The initial chapter reviews the essential material from functional analysis. New ideas are introduced along with their context. Proofs are detailed and carefully presented. The book concludes with a chapter on applications of the theory to Maxwell's equations and von Karman's equations. " -- Abebooks.com.
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- Initial value problems.
- Differential equations, Hyperbolic.
- Evolution equations.
- Hilbert space.
- Partial differential equations -- Hyperbolic equations and systems -- Initial value problems for second-order hyperbolic equations.
- Partial differential equations -- Hyperbolic equations and systems -- Quasilinear second-order hyperbolic equations.
- Partial differential equations -- Parabolic equations and systems -- Initial value problems for second-order parabolic equations.
- Partial differential equations -- Parabolic equations and systems -- Quasilinear parabolic equations.
- Partial differential equations -- Equations of mathematical physics and other areas of application -- Maxwell equations.
- Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with mechanics of deformable solids.
- Problèmes aux valeurs initiales.
- Équations différentielles hyperboliques.
- Équations d'évolution.
- Hilbert, Espaces de.