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THE DIRICHLET PROBLEM II. LIMIT SOLUTIONS, VERY WEAK SOLUTIONS AND SOME OTHER VARIANTS

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/9780198569039.003.0006
Subject:
Mathematics, Mathematical Physics

This chapter continues the analysis of the initial and boundary value problem. Topics covered include limit solutions, theory of very weak solutions, problems in different domains, limit solutions to ... More


Numerical results on shape optimization

Bijan Mohammadi and Olivier Pironneau

in Applied Shape Optimization for Fluids

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199546909
eISBN:
9780191720482
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199546909.003.0010
Subject:
Mathematics, Mathematical Physics

This chapter gathers some applications for stationary flows in two and three dimensions in space of shape optimization using the ingredients of this book. The configurations range from inviscid and ... More


Domain of Influence Theorems

Józef Ignaczak and Martin Ostoja‐Starzewski

in Thermoelasticity with Finite Wave Speeds

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199541645
eISBN:
9780191716164
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199541645.003.0004
Subject:
Mathematics, Applied Mathematics, Mathematical Physics

The first part of this chapter concerns a domain of influence theorem for a potential‐temperature problem, which is a particular form of a displacement‐temperature problem in the L‐S theory. The ... More


Kleinian groups

Jacques Franchi and Yves Le Jan

in Hyperbolic Dynamics and Brownian Motion: An Introduction

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199654109
eISBN:
9780191745676
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199654109.003.0004
Subject:
Mathematics, Mathematical Physics

This chapter deals with the geometric theory of Kleinian groups and their fundamental domains. It begins with the example of the parabolic tessellation of the hyperbolic plane by means of 2n-gons ... More


The role of numerical simulations

P. A. Davidson

in Turbulence: An Introduction for Scientists and Engineers

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198722588
eISBN:
9780191789298
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198722588.003.0007
Subject:
Mathematics, Applied Mathematics, Mathematical Physics

Chapter 7 discusses the role of numerical simulations in turbulence. The emphasis is on the new physical insights these numerical experiments have yielded, as well as some of the limitations of ... More


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