Petrovsky I.G. Lectures on Partial Differential Equations

Springer, 2008. - 204 Pages. This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods...

Academic Press, 1991. - 365 pages. This volume is representative of the lectures given at the International Conference on Differential Equations and Mathematical Physics, held at the University of Alabama at Birmingham on March 15-21 1990. It features plenary lectures on topics at the frontier of present day research, focusing on recent developments in the theory of ordinary and partial differential equations, both linear and non-linear, with pa...

CRC, 2005. - 304 Pages. Separation of Variables for Partial Differential Equations: An Eigenfunction Approach includes many realistic applications beyond the usual model problems. The book concentrates on the method of separation of variables for partial differential equations, which remains an integral part of the training in applied mathematics. The presentation includes, beyond the usual model problems, a number of realistic applications that...

Cambridge University Press, 1975. - 292 p. In this book, Professor Copson gives a rigorous account of the theory of partial differential equations of the first order and of linear partial differential equations of the second order, using the methods of classical analysis. In spite of the advent of computers and the applications of the methods of functional analysis to the theory of partial differential equations, the classical theory retains its...

Nova Science Publishers, 2008. - 304 pages. The theory of partial differential equations of mathematical physics has been one of the most important fields of study in applied mathematics. This is essentially due to the frequent occurrence of partial differential equations in many branches of natural sciences and engineering. The present lecture notes have been written for the purpose of presenting an approach based mainly on the mathematical pro...

Sрringer, 1984. - 530 pages. This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It is suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year'...

Academic Press, 2002. - 394 Pages. This book is written to meet the needs of undergraduates in applied mathematics, physics and engineering studying partial differential equations. Many books deal with partial differential equations, some at an elementary level and others at more advanced levels, so it is necessary that some justification should be given for the publication of another introductory text. With few exceptions, existing texts writt...

American Mathematical Society, 1986. - 100 Pages. The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations. An expanded version of the author's 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, multiple crit...

Springer, 2010. - 715 Pages. The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear d...

Springer, 1999. - 563 pages. This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic probl...