Publisher's Synopsis
Two general questions regarding partial differentialequations are explored in detail in this volume of theEncyclopaedia. The first is the Cauchy problem, and itsattendant question of well-posedness (or correctness). Theauthors address this question in the context of PDEs withconstant coefficients and more general convolutionequations in the first two chapters. The third chapterextends a number of these results to equations with variablecoefficients.The second topic is the qualitative theory of second orderlinear PDEs, in particular, elliptic and parabolicequations. Thus, the second part of the book is primarily alook at the behavior of solutions of these equations.There are versions of the maximum principle, thePhragmen-Lindelf theorem and Harnack's inequality discussedfor both elliptic and parabolic equations.The book is intended for readers who are already familiarwith the basic material in the theory of partialdifferential equations.
