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The Porous Medium EquationMathematical Theory$
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Juan Luis Vazquez

Print publication date: 2006

Print ISBN-13: 9780198569039

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198569039.001.0001

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INTRODUCTION

INTRODUCTION

Chapter:
(p.1) 1 INTRODUCTION
Source:
The Porous Medium Equation
Author(s):

Juan Luis Vázquez

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198569039.003.0001

This chapter introduces the mathematical theory of the nonlinear heat equation referred to as the porous medium equation (PME). This equation is one of the simplest examples of a nonlinear evolution equation of parabolic type. The peculiar features of the PME and nonlinear diffusion are discussed. An overview of the chapters in this volume is presented.

Keywords:   porous medium equation, heat equation, linear differential equations, nonlinear diffusion

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