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Bibliographic Details
Main Authors:	Sabel'fel'd, Karl K. 1953- (Author), Šalimova, I.A. 1962- (Author)
Format:	Book
Language:	English
Published:	[Berlin] De Gruyter 2016
Edition:	Reprint
Subjects:	Randwertproblem Partielle Differentialgleichung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029909207&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	Reprint der Ausgabe der Verlags VSP, Utrecht 1997
Physical Description:	viii, 188 Seiten Diagramme
ISBN:	9783110460568

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MARC


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Record in the Search Index

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adam_text	C O N TE N TS 1. INTRODUCTION 1 2. SCALAR SECOND ORDER PD E S 5 2.1. SPHERICAL MEAN VALUE RELATIONS FOR THE LAPLACE EQUATION AND INTEGRAL FORMULATION OF THE DIRICHLET P RO B LE M .................... 5 2.1.1. DIRECT SPHERICAL MEAN VALUE RE LA TIO N ...................... 6 2.1.2. CONVERSE MEAN VALUE THEOREM .................................. 13 2.1.3. INTEGRAL EQUATION EQUIVALENT TO THE DIRICHLET PROBLEM 15 2.1.4. POISSON-JENSEN FO R M U LA ........................................... 17 2.2. THE DIFFUSION AND HELMHOLTZ EQUATIONS ............................. 19 2.2.1. DIFFUSION E Q U A TIO N .................................................... 20 2.2.2. HELMHOLTZ EQUATION ................................................. 21 2.3. GENERALIZED SECOND ORDER ELLIPTIC E Q U A TIO N S ...................... 23 2.4. PARABOLIC E Q U A TIO N S .............................................................. 26 2.4.1. HEAT EQUATION.............................................................. 26 2.4.2. PARABOLIC EQUATIONS WITH VARIABLE COEFFICIENTS . . . 32 2.4.3. EXPANSION OF THE PARABOLIC M E A N S ......................... 35 3. H IGH-ORDER ELLIPTIC EQUATIONS 39 3.1. BALAYAGE O P E R A TO R ................................................................. 39 3.2. THE BIHARMONIC E Q U A TIO N ..................................................... 41 3.2.1. DIRECT SPHERICAL MEAN VALUE RE LA TIO N ...................... 42 3.2.2. THE GENERALIZED POISSON FO R M U LA ............................ 44 3.2.3. RIGID FIXING OF THE B O U N D A R Y .................................. 49 3.2.4. NONHOMOGENEOUS BIHARMONIC EQ U ATIO N ................... 52 3.3. FOURTH ORDER EQUATION GOVERNING THE BENDING OF A PLATE ON AN ELASTIC BASE S U RFA C E ........................................................... 54 3.4. METAHARMONIC EQUATIONS........................................................ 59 3.4.1. POLYHARMONIC EQUATION .............................................. 59 3.4.2. GENERAL C A S E .............................................................. 62 4. TRIANGULAR SYSTEM S OF ELLIPTIC EQUATIONS 68 4.1. A ONE-COMPONENT DIFFUSION S Y S TE M ..................................... 68 4.2. A TWO-COMPONENT DIFFUSION S Y S TE M ..................................... 70 4.3. A COUPLED BIHARMONIC-HARMONIC E Q U A TIO N ......................... 73 5. SYSTEM S O F ELASTICITY THEORY 75 5.1. THE LAME E Q U A TI O N .............................................................. 75 5.1.1. DIRECT SPHERICAL MEAN VALUE TH EO REM ...................... 75 5.1.2. CONVERSE SPHERICAL MEAN VALUE TH E O R E M ............... 81 5.2. PSEUDO-VIBRATION ELASTIC E Q U A T I O N ..................................... 84 5.3. THERMO-ELASTIC EQUATION .................................................... 92 6. T HE GENERALIZED POISSON FORMULA FOR TH E LAME EQUATION 94 6.1. PLANE E LA STIC ITY ....................................................................... 94 6.2. GENERALIZED SPATIAL POISSON FORMULA FOR THE LAME EQUATION 105 6.3. AN ALTERNATIVE DERIVATION OF THE POISSON FO RM U LA ................ 122 7. SPHERICAL M EANS FOR THE STRESS AND STRAIN TENSORS 127 7.1. SPHERICAL MEANS FOR THE DISPLACEMENT COMPONENTS THROUGH THE DISPLACEMENT V E C TO R ........................................................... 127 7.2. MEAN VALUE RELATION FOR THE STRESS AND STRAIN TENSORS THROUGH THE DISPLACEMENT V E C TO R ............................................................131 7.2.1. MEAN VALUE RELATION FOR THE STRAIN COMPONENTS . . 131 7.2.2. MEAN VALUE RELATION FOR THE STRESS COMPONENTS . . 137 7.3. MEAN VALUE RELATIONS FOR THE STRESS COMPONENTS IN TERMS OF THE SURFACE TRA C TIO N S ................................................................. 138 8. A PPLICATIONS TO TH E RANDOM WALK ON SPHERES M ETHOD 150 8.1. SPHERICAL MEAN AS A MATHEMATICAL E X P E C TA TIO N ................... 150 8.2. ITERATIONS OF THE SPHERICAL MEAN O P E R A TO R ............................ 151 8.3. THE RANDOM WALK ON SPHERES A LG O RITH M ............................ 152 8.3.1. THE RANDOM WALK ON SPHERES PROCESS FOR THE DIRICH- LET P RO B LE M .................................................................... 152 8.3.2. INHOMOGENEOUS C A S E .....................................................164 8.4. BIHARMONIC EQ U ATIO N ................................................................. 166 8.5. RANDOM WALK ON SPHERES METHOD FOR THE LAME EQUATION 168 8.5.1. NAIVE GENERALIZATION..................................................... 168 8.5.2. A MODIFICATION OF THE A LG O R ITH M ............................... 170 8.5.3. NON-ISOTROPIC RANDOM WALK ON S P H ERES ................... 173 8.5.4. BRANCHING P R O C E S S ........................................................ 175 8.5.5. ANALYTICAL CONTINUATION WITH RESPECT TO THE SPECTRAL P A RA M E TE R ....................................................................... 178 8.6. ALTERNATIVE SCHWARZ P RO C E D U RE ...............................................181 BIBLIOGRAPHY 185
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author	Sabel'fel'd, Karl K. 1953- Šalimova, I.A. 1962-
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dewey-tens	510 - Mathematics
discipline	Mathematik
edition	Reprint
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spellingShingle	Sabel'fel'd, Karl K. 1953- Šalimova, I.A. 1962- Spherical means for PDEs Randwertproblem (DE-588)4048395-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd
subject_GND	(DE-588)4048395-2 (DE-588)4044779-0
title	Spherical means for PDEs
title_auth	Spherical means for PDEs
title_exact_search	Spherical means for PDEs
title_full	Spherical means for PDEs K.K. Sabelfeld and I.A. Shalimova
title_fullStr	Spherical means for PDEs K.K. Sabelfeld and I.A. Shalimova
title_full_unstemmed	Spherical means for PDEs K.K. Sabelfeld and I.A. Shalimova
title_short	Spherical means for PDEs
title_sort	spherical means for pdes
topic	Randwertproblem (DE-588)4048395-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd
topic_facet	Randwertproblem Partielle Differentialgleichung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029909207&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT sabelfeldkarlk sphericalmeansforpdes AT salimovaia sphericalmeansforpdes

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