Partial Differential Equations III: The Cauchy Problem. Qualitative Theory of Partial Differential Equations

ISBN-13: 9783642634901 / Angielski / Miękka / 2012 / 197 str.

Yu V. Egorov; M. a. Shubin; M. Grinfeld

Opis

Two general questions regarding partial differential equations are explored in detail in this volume of the Encyclopaedia. The first is the Cauchy problem, and its attendant question of well-posedness (or correctness). The authors address this question in the context of PDEs with constant coefficients and more general convolution equations in the first two chapters. The third chapter extends a number of these results to equations with variable coefficients. The second topic is the qualitative theory of second order linear PDEs, in particular, elliptic and parabolic equations. Thus, the second part of the book is primarily a look at the behavior of solutions of these equations. There are versions of the maximum principle, the Phragmen-Lindel-f theorem and Harnack's inequality discussed for both elliptic and parabolic equations. The book is intended for readers who are already familiar with the basic material in the theory of partial differential equations.

Spis treści

I. The Cauchy Problem.- II. Qualitative Theory of Second Order Linear Partial Differential Equations.- Author Index.

O autorze

The mathematics in this volume of the Encyclopaedia, the third in the subseries on PDEs, is more advanced than that in EMS 30 (PDE I). The reader should already be familiar with what is found in that volume. EMS 32 covers in detail two very important topics in PDE: the Cauchy problem and the qualitative theory of second order linear equations. It should be of interest to advanced students and researchers in mathematics and to scientists in neighboring fields with strong mathematical backgrounds.