Spherical means for PDEs

Author(s)

• Sabelʹfelʹd, Karl Karlovich
• Shalimova, I. A.

Bibliographic Information

Spherical means for PDEs

K.K. Sabelfeld and I.A. Shalimova

VSP, 1997

Description and Table of Contents

Description

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 Lame equation, systems of diffusion and elasticity equations). In addition, applications to the random walk on spheres method are given.

Table of Contents

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 Lame equation Pseudo-vibration elastic equation Thermo-elastic equation GENERALIZED POISSON FORMULA FOR THE LAMe EQUATION Plane elasticity Generalized spatial Poisson formula for the Lame 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

by "Nielsen BookData"

Details

• NCID: BA31194368
• ISBN:
  • 9067642118
• Country Code: ne
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Utrecht
• Pages/Volumes: viii, 188 p.
• Size: 25 cm