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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. This book provides a presentation of the mathematical theory of the nonlinear heat equation 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 have been proposed in mathematical biology, lubrication, boundary ... More

*Keywords: *
heat equation,
linear partial differential equations,
nonlinear,
fluid flow,
heat transfer,
diffusion,
mathematical biology,
lubrication,
boundary layer theory

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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## Front Matter

## PART ONE

## PART TWO

## COMPLEMENTS

## End Matter

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