Degenerate Differential Equations in Banach Spaces

by Angelo Favini, Atsushi Yagi

Overview

This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.

Product Details

ISBN-13:	9781040212783
Publisher:	CRC Press
Publication date:	09/10/1998
Series:	Chapman & Hall/CRC Pure and Applied Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	336
File size:	871 KB

About the Author

Angelo Favini, Atsushi Yagi

Table of Contents

Preliminaries and notations; multivalued linear operators; degenerate equations of hyperbolic type; degenerate equations of parabolic type I; degenerate equations of parabolic type II; degenerate equations - the general case; degenerate differential equations of the second order; degenerate parabolic equations; bibliographical remarks.

Editorial Reviews

To readers familiar with some basic functional analysis, real and complex analysis, and partial differential equations, offers a detailed study of linear, abstract, degenerate differential equations and the regularity of their relations, using the semigroups generated by multi-valued, linear operators and extensions of the operational method of Da Prato and Grisvard. Among the topics are the analyticity of the semigroup generated by degenerate parabolic operations in spaces of continuous functions, the maximal regularity in time of solutions to degenerate equations of parabolic type in Banach spaces, the existence of regular solutions in contrast to the generalized solutions appearing in the literature, the multi-valued linear Cauchy problem in the hyperbolic and parabolic cases, and the regularity of semigroups generated by second-order degenerate parabolic operators in various function spaces. Annotation c. by Book News, Inc., Portland, Or.

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