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## PRELIMINARIES AND BASIC ESTIMATES

*Juan Luis Vázquez*

### in The Porous Medium Equation: Mathematical Theory

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198569039
- eISBN:
- 9780191717468
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198569039.003.0003
- Subject:
- Mathematics, Mathematical Physics

This chapter provides preliminary material on parabolic equations needed to develop the main theories of the book. It begins with a review of useful properties of quasilinear parabolic equations. ... More

## Introduction

*Juan Luis Vázquez*

### in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199202973
- eISBN:
- 9780191707919
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199202973.003.0001
- Subject:
- Mathematics, Applied Mathematics

This introductory chapter opens with an explanation of the purpose of the book, which is to obtain basic estimates for some particular nonlinear parabolic equations and to derive consequences about ... More

## Nonlinear Analysis of Time-Dependent Problems

*J. N. REDDY*

### in An Introduction to Nonlinear Finite Element Analysis

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198525295
- eISBN:
- 9780191711671
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525295.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this chapter, finite element models are used to solve time-dependent problems with nonlinearities and some standard time approximation schemes are described. All classes of nonlinear problems ... More

## Parabolic Equations

*Rüdiger Verfürth*

### in A Posteriori Error Estimation Techniques for Finite Element Methods

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199679423
- eISBN:
- 9780191758485
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199679423.003.0006
- Subject:
- Mathematics, Applied Mathematics, Numerical Analysis

We derive a posteriori error estimates for space–time finite element and certain finite volume discretisations of linear and nonlinear parabolic equations of second order. The starting point of our ... More

## A Posteriori Error Estimation Techniques for Finite Element Methods

*Rüdiger Verfürth*

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199679423
- eISBN:
- 9780191758485
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199679423.001.0001
- Subject:
- Mathematics, Applied Mathematics, Numerical Analysis

Self-adaptive discretization methods nowadays are an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to ... More

## The dimensions of time

*George Jaroszkiewicz*

### in Images of Time: Mind, Science, Reality

- Published in print:
- 2016
- Published Online:
- January 2016
- ISBN:
- 9780198718062
- eISBN:
- 9780191787553
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198718062.003.0012
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the mathematical reasons why time has one dimension rather than two or more dimensions. It examines the flow of information, through a spacetime with a given signature, in ... More

## Maximum Principles and Uniqueness Theorems

*Charles L. Epstein and Rafe1 Mazzeo*

### in Degenerate Diffusion Operators Arising in Population Biology (AM-185)

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691157122
- eISBN:
- 9781400846108
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691157122.003.0003
- Subject:
- Mathematics, Probability / Statistics

This chapter proves maximum principles for two parabolic and elliptic equations from which the uniqueness results follow easily. It also considers the main consequences of the maximum principle, both ... More

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