Progress in Nonlinear Analysis: Proceedings of the Second International Conference on Nonlinear Analysis Nankai University, Tianjin, China 14-19 June 1999 ... Applied Mathematics and Theoretical Physics)

This text has been designed for use on a one-year graduate course on boundary value problems for students of mathematics, engineering, and the physical sciences. It deals mainly with the three fundamental equations of mathematical physics, namely the heat equation, the wave equation, and Laplace's equation. The goal of the book is to obtain a formal solution to a given problem either by the method of separation of variables or by the method of general solutions, and to verify that the formal solution possesses all the required properties. To provide the mathematical justification for this approach, the theory of Sturm-Liouville problems, the Fourier series, and the Fourier transform are fully developed. The book assumes a knowledge of advanced calculus and elementary differential equations The real world is complicated, as a result of which most mathematical models arising from mechanics, physics, chemistry and biology are nonlinear. Based on the efforts of scientists in the 20th century, especially in the last three decades, topological, variational, geometrical and other methods have developed rapidly in nonlinear analysis, which made direct studies of nonlinear models possible in many cases, and provided global information on nonlinear problems which was not available by the traditional linearization method. This volume reflects that rapid development in many areas of nonlinear analysis. Presenting the papers from the 2nd International Conference on Nonlinear Analysis, held in June 1998, contributions to this volume explore the efforts of scientists in the last three decades of the 20th century within the field of nonlinear analysis.