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A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen

Differential equations, Partial. --- Differential equations, Nonlinear. --- Nonlinear differential equations --- Nonlinear theories --- Partial differential equations

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The problems treated in this volume concern nonlinear partial differential equations occurring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics. Presented are new results and new methods for analysis in bifurcation, singular perturbation, variational methods, stability analysis, rearrangement, energy inequalities, etc.

Differential equations, Partial. --- Differential equations, Nonlinear. --- Nonlinear differential equations --- Nonlinear theories --- Partial differential equations

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51 --- Differential equations, Nonlinear --- Differential equations, Partial --- Partial differential equations --- Nonlinear differential equations --- Nonlinear theories --- Mathematics --- 51 Mathematics

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This is an expanded fourth edition of a classic text, including numerous worked examples, diagrams and exercises. An ideal resource for students and lecturers in engineering, mathematics and the sciences, it is published alongside a separate Problems and Solutions Sourcebook with over 500 problems and solutions.

Differential equations, Nonlinear. --- Mathematics. --- Math --- Science --- Nonlinear differential equations --- Nonlinear theories --- Equations différentielles non linéaires

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This book is the first one devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. These processes are closely associated with nonlinear Ito's stochastic ordinary differential equations (ISODEs) and with the space-discretized versions of nonlinear Ito's stochastic partial integro-differential equations. The latter models include Ito's stochastic partial differential equations (ISPDEs). The book presents the new analytical treatment which can serve as the basis of a combined, analytical-numerical approach to greater computational efficie

Engineering --- Stochastic processes. --- Diffusion processes. --- Differential equations, Nonlinear. --- Nonlinear differential equations --- Nonlinear theories --- Markov processes --- Random processes --- Probabilities --- Mathematical models.