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The Cauchy Problem is written by Hector O. Fattorini and published by Cambridge University Press. It's available with International Standard Book Number or ISBN identification 0521302382 (ISBN 10) and 9780521302388 (ISBN 13).
This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.