Spherical Means for PDEs
VSP International Science Publishers (Verlag)
978-90-6764-211-8 (ISBN)
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01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information.
This monographs presents new spherical mean value relations for classical boundary value problems of mathematical physics. The derived spherical mean value relations provide equivalent integral formulations of original boundary value problems.
Direct and converse mean value theorems are proved for scalar elliptic equations (the Laplace, Helmholtz and diffusion equations), parabolic equations, high-order elliptic equations (biharmonic and metaharmonic equations), and systems of elliptic equations (the Lamé equation, systems of diffusion and elasticity equations). In addition, applications to the random walk on spheres method are given.
Introduction
SCALAR SECOND ORDER PDES
Spherical mean value relations for the Laplace equation and integral formulation of the Dirichlet problem
The diffusion and Helmholtz equations
Generalized second order elliptic equations
Parabolic equations
HIGH-ORDER ELLIPTIC EQUATIONS
Balayage operator
The biharmonic equation
Fourth order equation govering the bending of a plate on an elastic base surface
Metaharmonic equations
TRIANGULAR SYSTEMS OF ELLIPTIC EQUATIONS
A one-component diffusion system
A two-component diffusion system
A coupled biharmonic-harmonic equation
SYSTEMS OF ELASTICITY THEORY
The Lamé equation
Pseudo-vibration elastic equation
Thermo-elastic equation
GENERALIZED POISSON FORMULA FOR THE LAMé EQUATION
Plane elasticity
Generalized spatial Poisson formula for the Lamé equation
An alternative derivation of the Poisson formula
SPHERICAL MEANS FOR THE STRESS AND STRAIN TENSOR
Spherical means for the displacement components through the displacement vector
Mean value relations for the stress components in terms of the surface tractions
APPLICATIONS TO THE RANDOM WALK ON SPHERES METHOD
Spherical mean as mathematical expectation
Iterations of the spherical mean operator
Random walk on spheres algorithm
Biharmonic equation
Alternative Schwarz procedure
Bibliography
| Erscheint lt. Verlag | 1.3.1997 |
|---|---|
| Verlagsort | Zeist |
| Sprache | englisch |
| Gewicht | 455 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| ISBN-10 | 90-6764-211-8 / 9067642118 |
| ISBN-13 | 978-90-6764-211-8 / 9789067642118 |
| Zustand | Neuware |
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