03373nam 2200673 450 991080770720332120230803031948.03-11-031533-510.1515/9783110315332(CKB)2670000000495289(EBL)1524379(OCoLC)862612009(SSID)ssj0001041537(PQKBManifestationID)11681824(PQKBTitleCode)TC0001041537(PQKBWorkID)11010108(PQKB)11639906(MiAaPQ)EBC1524379(DE-B1597)209204(OCoLC)864085898(DE-B1597)9783110315332(Au-PeEL)EBL1524379(CaPaEBR)ebr10811336(CaONFJC)MIL808134(EXLCZ)99267000000049528920130725h20132013 uy 0engurnn#---|u||utxtccrSpherical and plane integral operators for PDEs construction, analysis, and applications /Karl K. Sabelfeld, Irina A. ShalimovaBerlin ;Boston :Walter de Gruyter GmbH & Company,[2013]©20131 online resource (338 p.)Description based upon print version of record.3-11-031529-7 Includes bibliographical references and index.Front matter --Preface --Contents --1. Introduction --2. Scalar second-order PDEs --3. High-order elliptic equations --4. Triangular systems of elliptic equations --5. Systems of elasticity theory --6. The generalized Poisson formula for the Lamé equation --7. Spherical means for the stress and strain tensors --8. Random Walk on Spheres method --9. Random Walk on Fixed Spheres for Laplace and Lamé equations --10. A stochastic spectral projection method for solving PDEs for some classes of domains --11. Stochastic boundary collocation and spectral methods --12. Solution of 2D elasticity problems with random loads --13. Boundary value problems for some elliptic PDEs with random boundary conditions --Bibliography --IndexThe book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.Differential equations, PartialIntegral operatorsBoundary value problems.Spectral projection method.Spherical integral operator.Stochastic numeric.Differential equations, Partial.Integral operators.515/.353SK 540rvkSabelʹfelʹd K. K(Karl Karlovich)1027546Shalimova I. A1607138MiAaPQMiAaPQMiAaPQBOOK9910807707203321Spherical and plane integral operators for PDEs3933277UNINA