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Introduction to Partial Differential Equations (Paperback)
by Nicolae H. Pavel
The aim of this short textbook (of about 210 pages) is to present some fundamental results from both classical and modern theory of PDE.
Some classical topics on PDE presented here are: Cauchy method of characteristics, Cauchy-Kowalevski¿s Theorem, Gauss law for a harmonic
function, maximum principles, Green¿s function, Poisson¿s kernel, Perron¿s method, the Wave Equation, D¿Alembert formula and spherical means,
solutions with compact support, the Heat Equation, the Fourier transform. Modern topics: Sobolev spaces and Green identities, the fundamental
solution of Laplace equation in terms of Dirac distribution, maximum principles via Stampacchia¿s method of truncation, the Co-semigroup
generated by Laplace operator in L2() and its smoothing effect on the initial data, Hille-Yosida¿s exponential formula and its nonlinear
version of Crandall-Liggett. Many examples and exercises, geometric and physical interpretations of the theory are included. A brief introduction
to the theory of distributions and four useful appendices have been added. About the author: NICOLAE H. PAVEL is Professor of Mathematics at Ohio
University, at Athens. He is the author/ coauthor of nine books and over 100 professional papers and the editor/coeditor of four international
conference proceedings. Dr.Pavel is a member of the AMS, the Secretary General of the American- Romanian Academy and a member of the Editorial
Board of fourteen professional journals. Dr.Pavel, a recipient of: the Simeon Stoilov Award from the Romanian Academy of Sciences, the
Distinguished Professor Award at the AL.I.CUZA University of Iasi, Doctor Honoris Causa (Honorary Degree) from Ovidius University of Constanta,
Romania, received the Ph.D. degree (1972) from the University of Iasi. Dr. Pavel has introduced new concepts such as the tangency to a set in the
sense of a semigroup, which is now named for him: Pavel¿s tangential condition.
ISBN-10: 0-9778102-3-2
ISBN-13: 978-0-9778102-3-9
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