Second Order Linear Differential Equations in Banach Spaces, Volume 108

1st Edition

Authors: H.O. Fattorini
Hardcover ISBN: 9780444876980
eBook ISBN: 9780080872193
Imprint: North Holland
Published Date: 1st January 1985
Page Count: 313
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Table of Contents

The Cauchy Problem for First Order Equations. Semigroup Theory. The Cauchy Problem for Second Order Equations. Cosine Function Theory. Reduction of a Second Order Equation to a First Order System. Phase Spaces. Applications to Partial Differential Equations. Uniformly Bounded Groups and Cosine Functions in Hilbert Space. The Parabolic Singular Perturbation Problems. Other Singular Perturbation Problems. The Complete Second Order Equation. Bibliography.


Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.


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© North Holland 1985
North Holland
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About the Authors

H.O. Fattorini Author

Affiliations and Expertise

University of California,Department of Mathematics