The Cauchy Problem
Encyclopedia of Mathematics and its Applications Series

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.

Editor's statement; Foreword; Preface; 1. Elements of functional analysis; 2. The caucy problem for some equations of mathematical physics: the abstract cauchy problem; 3. Properly posed cauchy problems: general theory; 4. Dissipative operators and applications; 5. Abstract parabolic equations: applications to second order parabolic equations; 6. Perturbation and approximation of abstract differential equations; 7. Some improperly posed cauchy problems; 8. The abstract cauchy problem for time-dependent equations; 9. The cauchy problem in the sense of vector-valued distributions; References; Index.

Hector O. Fattorini graduated from the Licenciado en Matemática, Universidad de Buenos Aires in 1960 and gained a Ph.D. in Mathematics from the Courant Institute of Mathematical Sciences, New York University, in 1965. Since 1967, he has been a member of the Department of Mathematics at the University of California, Los Angeles.