General Parabolic Mixed Order Systems in Lp and Applications (Hardcover, 2013 ed.)

In this text, a theory for general linear parabolic partial differential equations is established which covers equations with inhomogeneous symbol structure as well as mixed-order systems. Typical applications include several variants of the Stokes system and free boundary value problems. We show well-posedness in "Lp-Lq"-Sobolev spaces in time and space for the linear problems (i.e., maximal regularity) which is the key step for the treatment of nonlinear problems. The theory is based on the concept of the Newton polygon and can cover equations which are not accessible by standard methods as, e.g., semigroup theory. Results are obtained in different types of non-integer "Lp"-Sobolev spaces as Besov spaces, Bessel potential spaces, and Triebel Lizorkin spaces. The last-mentioned class appears in a natural way as traces of "Lp-Lq"-Sobolev spaces. We also present a selection of applications in the whole space and on half-spaces. Among others, we prove well-posedness of the linearizations of the generalized thermoelastic plate equation, the two-phase Navier Stokes equations with Boussinesq Scriven surface, and the "Lp-Lq" two-phase Stefan problem with Gibbs Thomson correction. "

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Operator Theory: Advances and Applications, 239
Release date:	December 2013
First published:	2013
Authors:	Robert Denk • Mario Kaip
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Hardcover
Pages:	250
Edition:	2013 ed.
ISBN-13:	978-3-319-01999-4
Categories:	Books > Science & Mathematics > Physics > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis Books > Science & Mathematics > Mathematics > Applied mathematics > General
LSN:	3-319-01999-6
Barcode:	9783319019994

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