A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations. These approaches, in conjunction with modern computational methods, help solve physical problems in a satisfactory manner. The asymptotic methods dealt with here include self-similarity, balancing argument, and matched asymptotic expansions. The physical models discussed in some detail here relate to porous media equation, heat equation with absorption, generalized Fisher's equation, Burgers equation and its generalizations. A chapter each is devoted to nonlinear diffusion and fluid mechanics. The present book will be found useful by applied mathematicians, physicists, engineers and biologists, and would considerably help understand diverse natural phenomena.
The present authors have been engaged in the study – both analytical and numerical – of large time asymptotic behaviour of nonlinear partial differential equations (PDEs) for many years. They had considerable interaction on this subject with Professor B. Enflo, KTH, Stockholm and Professor R. E. Grundy, University of St. Andrews, St. Andrews. Their contribution is gratefully acknowledged. The present venture was embarked upon while the first author (PLS) was Senior Scientist (Indian National Science Academy) at the Department of Mathematics, Indian Institute of Science, Bangalore, and was completed when he moved to the Department of Mathematics, University of Delhi, South Campus. He wishes to thank both the IISc and the University of Delhi for the facilities and to INSA for financial support. The second author (ChSR) is grateful to the Indian Institute of Technology Madras, Chennai for the financial support under Golden Jubilee book writing and new faculty schemes as he worked on this monograph. The authors also acknowledge the efforts of Professor K. T. Joseph, Tata Institute of Fundamental Research, Bombay and Mr. Manoj Kumar Yadav, IIT Madras, who carefully went through some parts of this book.
