Porous Medium Equation Mathematical Theory

Name: Porous Medium Equation Mathematical Theory
Availability: OutOfStock
ISBN: 9780198569039

ISBN-10: 0198569033

ISBN-13: 9780198569039

Edition: 2006

Authors: Juan Luis Vazquez

List price: $190.00

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The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood. In this monograph, aimed at research students and academics in mathematics and engineering, as well as engineering specialists, Professor Vazquez provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heatequation usually called the Porous Medium Equation (PME). This equation appears in a number of physical applications, such as to describe processes involving fluid flow, heat transfer or diffusion. Other applications…

Book details

List price: $190.00
Copyright year: 2006
Publisher: Oxford University Press, Incorporated
Publication date: 12/28/2006
Binding: Hardcover
Pages: 648
Size: 6.14" wide x 9.21" long x 1.57" tall
Weight: 2.332
Language: English



Preface



Introduction






Main applications



Preliminaries and basic estimates



Basic examples



The Dirichlet problem



Weak solutions



The Dirichlet problem



Limit solutions, very weak solutions and some other variants



Continuity of local solutions



The Dirichlet problem



Strong solutions



The Cauchy problem. L' theory



The PME as an abstract evolution equation. Semigroup approach



The Neumann problem and problems on manifolds






The Cauchy problem with growing initial data



Optimal existence theory for nonnegative solutions



Propagation properties



One-dimensional theory


Regularity and interfaces



Full analysis of selfsimilarity



Techniques of symmetrization and concentration



Asymptotic behaviour



The Cauchy problem



Regularity and finer asymptotics in several dimensions



Asymptotic behaviour



Dirichlet and Neumann problemsComplements



Further applications



Basic facts and appendices


Bibliography


Index