Linear and Quasilinear Parabolic Problems: Volume I: Abstract Linear Theory: 89 (Monographs in Mathematics) - Softcover

Buch 7 von 29: Monographs in Mathematics

Amann, Herbert

 
9783034899505: Linear and Quasilinear Parabolic Problems: Volume I: Abstract Linear Theory: 89 (Monographs in Mathematics)
Softcover
ISBN 10: 3034899505 ISBN 13: 9783034899505
Verlag: Birkhäuser, 2011

Inhaltsangabe

In this treatise we present the semigroup approach to quasilinear evolution equa­ of parabolic type that has been developed over the last ten years, approxi­ tions mately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather ’nonstandard’ type. In partic­ ular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille­ Yosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Reseña del editor

In this treatise we present the semigroup approach to quasilinear evolution equa­ of parabolic type that has been developed over the last ten years, approxi­ tions mately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In partic­ ular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille­ Yosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory.

Reseña del editor

This treatise gives an exposition of the functional analytical approach to quasilinear parabolic evolution equations, developed to a large extent by the author during the last 10 years. This approach is based on the theory of linear nonautonomous parabolic evolution equations and on interpolation-extrapolation techniques. It is the only general method that applies to noncoercive quasilinear parabolic systems under nonlinear boundary conditions. The present first volume is devoted to a detailed study of nonautonomous linear parabolic evolution equations in general Banach spaces. It contains a careful exposition of the constant domain case, leading to some improvements of the classical Sobolevskii-Tanabe results. It also includes recent results for equations possessing constant interpolation spaces. In addition, systematic presentations of the theory of maximal regularity in spaces of continuous and Hölder continuous functions, and in Lebesgue spaces, are given. It includes related recent theorems in the field of harmonic analysis in Banach spaces and on operators possessing bounded imaginary powers. Lastly, there is a complete presentation of the technique of interpolation-extrapolation spaces and of evolution equations in those spaces, containing many new results.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Birkhäuser
Erscheinungsdatum
2011
Sprache
Englisch
ISBN 10 
3034899505
ISBN 13 
9783034899505
Einband
Tapa blanda
Anzahl der Seiten
380
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar

Weitere beliebte Ausgaben desselben Titels

9783764351144: Linear and Quasilinear Parabolic Problems: Volume I: Abstract Linear Theory: 89 (Monographs in Mathematics)

Vorgestellte Ausgabe

ISBN 10:  3764351144 ISBN 13:  9783764351144
Verlag: Birkhäuser, 1995
Hardcover