Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book is concerned with basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. This is a monograph about the most significant results obtained in this area in last decades but is also written as a graduate textbook on modern methods in partial differential equations with main emphasis on applications to fundamental mathematical models of mathematical physics, fluid dynamics and mechanics. This book is selfcontained while the prerequisites in functional analysis are necessary to understand as it is being presented in a preliminary chapter. An up-to-date list of references and extended comments are included.

Banach spaces. --- Banach-Raum. --- Differential equations, Nonlinear. --- Banach spaces --- Differential equations, Nonlinear --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Nonlinear differential equations --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Physics. --- Analysis. --- Partial Differential Equations. --- Theoretical, Mathematical and Computational Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Partial differential equations --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Nonlinear theories --- Functions of complex variables --- Generalized spaces --- Topology --- Global analysis (Mathematics). --- Differential equations, partial. --- Analysis, Global (Mathematics) --- Differential topology --- Geometry, Algebraic --- Mathematical physics. --- Physical mathematics --- Physics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Differential equations, Nonlinear -- Asymptotic theory. --- Differential equations, Partial. --- Functional analysis. --- Linear operators. --- Differential equations, Nonlinear --- Mathematics --- Calculus --- Physical Sciences & Mathematics --- Asymptotic theory --- Mathematical analysis. --- Asymptotic theory. --- 517.1 Mathematical analysis --- Mathematical analysis --- Asymptotic theory in nonlinear differential equations --- Mathematics. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Physics. --- Continuum physics. --- Partial Differential Equations. --- Mathematical Methods in Physics. --- Classical Continuum Physics. --- Applications of Mathematics. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Engineering --- Engineering analysis --- Partial differential equations --- Math --- Science --- Asymptotic expansions --- Differential equations, partial. --- Mathematical physics. --- Classical and Continuum Physics. --- Physical mathematics