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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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