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The Porous Medium Equation: Mathematical Theory

Juan Luis Vazquez

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198569039
eISBN:
9780191717468
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198569039.001.0001
Subject:
Mathematics, Mathematical Physics

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 ... More


Dynamics of Viscous Compressible Fluids

Eduard Feireisl

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198528388
eISBN:
9780191713590
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528388.001.0001
Subject:
Mathematics, Applied Mathematics

The book presents and develops the most recent ideas and concepts of the mathematical theory of viscous, compressible, and heat conducting fluids. Two main objectives are pursued: (i) global ... More


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

Juan Luis Vázquez

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.001.0001
Subject:
Mathematics, Applied Mathematics

This book is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as ... More


Heat

Stephen J. Blundell and Katherine M. Blundell

in Concepts in Thermal Physics

Published in print:
2009
Published Online:
January 2010
ISBN:
9780199562091
eISBN:
9780191718236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562091.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter explores the concepts of heat and heat capacity. Heat is defined as 'thermal energy in transit'. The heat capacity C of an object is given by C = dQ/dT. The heat capacity of a substance ... More


An Introduction to Nonlinear Finite Element Analysis

J. N. Reddy

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of ... More


The heat treatment of invar

Robert James Matthys

in Accurate Clock Pendulums

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198529712
eISBN:
9780191712791
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529712.003.0022
Subject:
Physics, History of Physics

Even though invar is the most common material used for the pendulum rod in a good clock, it is still a poor material for the purpose because of its relatively poor dimensional stability over time ... More


Thermal waves and ablative drive

Stefano Atzeni and JÜrgen Meyer-Ter-Vehn

in The Physics of Inertial Fusion: BeamPlasma Interaction, Hydrodynamics, Hot Dense Matter

Published in print:
2004
Published Online:
January 2008
ISBN:
9780198562641
eISBN:
9780191714030
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198562641.003.0007
Subject:
Physics, Nuclear and Plasma Physics

Energy transport in ICF targets is dominated by electron heat conduction and radiative energy transfer. This transport often occurs in form of thermal waves with steep fronts, which may run ... More


On the Early Work of William Thomson: Mathematical Physics and Methodology in the 1840s

I. Grattan-Guinness

in Kelvin: Life, Labours and Legacy

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199231256
eISBN:
9780191710803
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199231256.003.0003
Subject:
Mathematics, History of Mathematics

This chapter reviews the early works of William Thomson. Thomson began to publish exceptionally early, in 1841, while still in his late teens; and a steady stream of papers came from him thereafter. ... More


‘A Dynamical Form of Mechanical Effect’: Thomson's Thermodynamics

Iwan Rhys Morus

in Kelvin: Life, Labours and Legacy

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199231256
eISBN:
9780191710803
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199231256.003.0008
Subject:
Mathematics, History of Mathematics

As he settled into his position as Professor of Natural Philosophy at Glasgow, Thomson would spend much of his time over the subsequent years pondering over the problem of heat and the difficulty of ... More


Kelvin and Engineering

Bernard Crossland

in Kelvin: Life, Labours and Legacy

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199231256
eISBN:
9780191710803
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199231256.003.0009
Subject:
Mathematics, History of Mathematics

This chapter focuses on the achievements of Lord Kelvin as one of the great engineers of the 19th century. Topics discussed include his interest in laying a transatlantic telegraph cable, his ... More


PROPAGATION PROPERTIES

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/9780198569039.003.0014
Subject:
Mathematics, Mathematical Physics

This chapter introduces a study of the properties of the support and the free boundary of the solution in a several dimensional setting. It discusses in detail the property of finite propagation and ... More


INTRODUCTION

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/9780198569039.003.0001
Subject:
Mathematics, Mathematical Physics

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 ... More


MAIN APPLICATIONS

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/9780198569039.003.0002
Subject:
Mathematics, Mathematical Physics

This chapter reviews the main applications of the porous medium equation (PME). Section 2.1 describes the standard model of gas flow through a porous medium (Darcy-Leibenzon-Muskat). Section 2.2 ... More


The Sun's Influence on Climate

Joanna D. Haigh and Peter Cargill

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691153834
eISBN:
9781400866540
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153834.001.0001
Subject:
Environmental Science, Climate

The Earth's climate system depends entirely on the Sun for its energy. Solar radiation warms the atmosphere and is fundamental to atmospheric composition, while the distribution of solar heating ... More


Computations, Transition Formulae, and the Local Index Formula

Simon Scott

in Traces and Determinants of Pseudodifferential Operators

Published in print:
2010
Published Online:
January 2011
ISBN:
9780198568360
eISBN:
9780191594748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568360.003.0004
Subject:
Mathematics, Analysis

In this chapter the constructions of chapters 1 and 2 for are illustrated with explicit computations. The first part of the chapter presents various methods of computation commonly used in the ... More


The Intransigence of Things

Stephen J. Collier

in Post-Soviet Social: Neoliberalism, Social Modernity, Biopolitics

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691148304
eISBN:
9781400840427
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691148304.003.0008
Subject:
Anthropology, Social and Cultural Anthropology

This chapter looks at the reform of communal services, particularly centralized heating systems. The heating system was a key element of the Soviet variant of “infrastructural” social modernity. ... More


Lower bounds, contractivity, error estimates, and continuity

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/9780199202973.003.0005
Subject:
Mathematics, Applied Mathematics

This chapter considers a number of bounds that complement the study so far, which was centred on upper bounds. The first section concerns the existence of lower bounds for non-negative solutions. ... More


General Physiological Principles

J. Eduardo P. W. Bicudo, William A. Buttemer, Mark A. Chappell, James T. Pearson, and Claus Bech

in Ecological and Environmental Physiology of Birds

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199228447
eISBN:
9780191711305
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228447.003.0002
Subject:
Biology, Ornithology

Birds show a number of structural and functional adaptations that are characteristic of the group as a whole and independent of the ability to fly. This chapter explores some basic physical and ... More


Adaptations: Living in Specific Environments

J. Eduardo P. W. Bicudo, William A. Buttemer, Mark A. Chappell, James T. Pearson, and Claus Bech

in Ecological and Environmental Physiology of Birds

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199228447
eISBN:
9780191711305
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228447.003.0005
Subject:
Biology, Ornithology

Birds are found in essentially all terrestrial environments, from lush tropical forests to barren deserts and polar regions, from the oceans to the highest mountains. This chapter describes how birds ... More


Lethal temperature limits

Steven L. Chown and Sue W. Nicolson

in Insect Physiological Ecology: Mechanisms and Patterns

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198515494
eISBN:
9780191705649
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198515494.003.0005
Subject:
Biology, Animal Biology

Temperature change has an effect on many physiological processes and insects frequently evolve strategies to overcome the rate, sub-lethal or lethal effects of temperature variation. This chapter ... More


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