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Spherical means for PDEs

Author: K K Sabelʹfelʹd; I A Shalimova
Publisher: Utrecht, Netherlands : VSP, 1997.
Edition/Format:   Print book : EnglishView all editions and formats

This monograph presents new spherical mean-value relations for classical boundary value problems of mathematical physics. The derived spherical mean value relations provide equivalent integral  Read more...


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Document Type: Book
All Authors / Contributors: K K Sabelʹfelʹd; I A Shalimova
ISBN: 9067642118 9789067642118
OCLC Number: 37145147
Description: viii, 188 pages ; 25 cm
Contents: Part 1 Scalar second-order PDEs: spherical mean-value relations for the Laplace equation and integral formulation of the Dirichlet problem; direct spherical mean-value relation; converse mean-value theorem; integral equation equivalent to the Dirichlet problem; Poisson-Jensen formula; the diffusion and Helmholtz equations; diffusion equation; Helmholtz equation; generalized second-order elliptic equations; parabolic equations; heat equation; parabolic equation with variable co-efficients; expansion of the parabolic means. Part 2 High-order elliptic equations: Balayage operator; the biharmonic equation; direct spherical mean-value relation; the generalized Poisson formula; rigid fixing of the boundary; non-homogeneous biharmonic equation; fourth-order equation governing the bending of a plate on an elastic base surface; metaharmonic equations; polyharmonic equation; general case. Part 3 Triangular systems of elliptic equations: a one-component diffusion system; a two-component diffusion system; a coupled biharmonic-harmonic equation. Part 4 Systems of elasticity theory: the Lame equation; direct spherical mean-value theorem; converse spherical mean-value theorem; pseudo-vibration elastic equation; thermo-elastic equation. Part 5 The generalized Poisson formula for the Lame equation: plane elasticity; generalized spatial Poisson formula for the Lame equation; an alternative derivation of the Poisson formula. Part 6 Spherical means for the stress and strain tensors. Part 7 Applications to the random-walk-on-spheres method. (Part contents)
Responsibility: K.K. Sabelʹfelʹd and I.A. Shalimova.
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