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Table of Contents
Preface
Introduction
Chapter I. The Origins of Free and Moving Boundary Problems
1. FREE AND MOVING BOUNDARY PROBLEMS INDUCED BY THE PHYSICAL
INACCEPTABILITY OF SOLUTIONS OF THE UNDERLYING DIFFERENTIAL
EQUATIONS: SHOCK WAVES
2. FREE AND MOVING BOUNDARY PROBLEMS INDUCED BY A SUDDEN CHANGE
IN PHYSICAL PROPERTIES
A. Frictional and Contact Problems in Solid Mechanics
B. Problems in Heat Conduction
C. Problems in Molecular Diffusion
D. Problems in Incompressible Hydrodynamics
(a) Inviscid Flow
(b) Slow Flow
E. Problems in Porous Media
3. FURTHER REMARKS
Chapter II. Intuitive Ideas about Weak and Variational Methods
1. REFORMULATION OF FREE AND MOVING BOUNDARY PROBLEMS
(i) Integral Equation Methods
(ii) Mapping Methods
(iii) Discretisations
(iv) Embedding and Fixed Domain Methods
2. WEAK FORMULATION OF FREE AND MOVING BOUNDARY PROBLEMS
(i) Problems of Type 1 (p. 4)
(ii) Problems of Type 2 (p. 6)
(a) The Porous Medium Equation
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