UID:
almahu_9949697882502882
Umfang:
1 online resource (447 p.)
ISBN:
1-281-76643-7
,
9786611766436
,
0-08-087312-X
Serie:
Pure and applied mathematics; a series of monographs and textbooks, v. 4
Inhalt:
Kernel functions and differential equations
Anmerkung:
Description based upon print version of record.
,
Front Cover; Kernel Functions and Elliptic Differential Equations in Mathematical Physics; Copyright Page; Contents; Preface; Note to the Reader; Part A: Boundary Value Problems for Partld Dlfferentlal EquaUonr of Elllptlc Type; CHAPTER I: THEORY OF HEAT CONDUCTION; 1. The differential equation of heat transfer; 2. The special case of steady flow; 3. Point sources and fundamental singularities; 4. Fundamental solutions; 5. Discontinuities; 6. Dirichlet's principle; 7. A modified heat equation; 8. Formal considerations; CHAPTER II: FLUID DYNAMICS; 1. The fundamental equations
,
2. Stationary irrotational flow3. Incompressible, irrotational, stationary fluid flow; 4. Sources and sinks; 5. Fundamental solutions and flow patterns; 6. Infinite domains; 7. Virtual mass; 8. Dirichlet identities; 9. Virtual mass as an extremum; 10. Variational formulas; 11. Free boundaries, discontinuity surfaces, and virtual mass; 12. Two-dimensional flows; 13. Boundary value problems and fundamental solutions in plane flows; 14. Obstacles in a plane flow; 15. The variation of the Green's function; 16. Lavrentieff's extremum problem for lift; 17. Free boundaries in plane flow
,
18. The complex kernel function and its applications19. Axially symmetric motion of an incompressible fluid; 20. Associated partial differential equations; 21. Two-dimensional compressible fluid flow; 22. Construction of solutions of the differential equations in the hodograph plane; 23. The hodograph method and boundary value problems in the physical plane; 24. Singularities in the hodograph plane and their application; CHAPTER III: ELECTRO- AND MAGNETOSTATICS; 1. The general equations of the electrostatic field; 2. Conductor potentials and induction coefficients
,
3. The energy of the electrostatic field4. The magnetostatic field; 5. The conductor potential; spherical harmonics; 6. Polarization of a conducting surface; 7. Forces and moments in a conductor surface; 8. Orthogonal harmonic functions; CHAPTER IV: ELASTICITY; 1. Strain tensor fields; 2. Stress tensor fields; 3. Stress-strain relations; 4. The energy integral and boundary value problems; 5. Betti's formula and the fundamental singularity; 6. Fundamental solutions; 7. Construction of the fundamental solutions in terms of orthonormal solution fields; 8. Particular solutions
,
9. The theory of thin plates10. Fundamental solutions of the biharmonic equation; 11. Plane strain; Part B: Kernel Function Methods in the Theory of Boundary Value Problems; CHAPTER I : PROPERTIES OF SOLUTIONS; 1. Introduction; 2. Notation and definitions; 3. Properties OI the solutions of (1.1); 4. Existence theorems for certain solutions; 5. Fundamental singularities and fundamental solutions; 6. Dirichlet integrals and fundamental functions; CHAPTER II: THE KERNEL FUNCTIONS AND THEIR PROPERTIES; 1. Kernel functions; 2. Orthonormal systems and construction of the kernel
,
3. Integral operators and the construction of complete sets of solutions
,
English
Weitere Ausg.:
ISBN 0-12-374581-0
Sprache:
Englisch
Bookmarklink
