Author | Kythe, Prem K. author |
---|---|
Title | Fundamental Solutions for Differential Operators and Applications [electronic resource] / by Prem K. Kythe |
Imprint | Boston, MA : Birkhรคuser Boston, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4106-5 |
Descript | XXIV, 414 p. online resource |
1. Historical Background -- 2. Modern Developments -- 1: Some Basic Concepts -- 1.1. Definitions -- 1.2. Greenโs Identities -- 1.3. Distributions -- 1.4. Fundamental Solutions -- 2: Linear Elliptic Operators -- 2.1. Constant Coefficients -- 2.2. Laplace Operator -- 2.3. Helmholtz Operator -- 2.4. Cauchy-Riemann Operator -- 2.5. Nonhomogeneous Operator -- 2.6. Maximum Principle -- 2.7. Method of Images -- 3: Linear Parabolic Operators -- 3.1. Diffusion Operator -- 3.2. Heat Potentials -- 3.3. Cauchy Problem -- 3.4. Maximum Principle -- 3.5. Schrรถdinger Operator -- 3.6. Method of Images -- 4: Linear Hyperbolic Operators -- 4.1. Wave Operator -- 4.2. Harmonie Oscillators -- 4.3. Wave Potentials -- 4.4. Cauchy Problem -- 4.5. Wave Propagation -- 4.6. Maxwellโs Equations -- 5: Nonlinear Operators -- 5.1. Einstein-Kolmogorov Operator -- 5.2. Fokker-Plank Operator -- 5.3. Klein-Gordon Operator -- 5.4. Diracโs Operator -- 5.5. Transport Equation -- 5.6. Transport Operator -- 5.7. Biharmonic Operator -- 5.8. Nonlinear Wave Equations -- 5.9. The ?-function -- 5.10. Quasihyperbolic Operator -- 6: Elastostatics -- 6.1. Basic Relations -- 6.2. Cauchy-Navier Operator -- 6.3. Half-Space Solutions -- 6.4. Axisymmetric Solutions -- 6.5. Somiglianaโs Identity -- 7: Elastodynamics -- 7.1. Elastodynamic Operator -- 7.2. Wave Structures -- 7.3. Bernoulli-Euler Operator -- 7.4. Elastoplasticity -- 7.5. Anisotropic Medium -- 8: Fluid Dynamics -- 8.1. Navier-Stokes Equations -- 8.2. Aerodynamic Flows -- 8.3. Non-Newtonian Flows -- 8.4. Porous Media -- 8.5. Underwater Acoustic Scattering -- 9: Piezoelectrics -- 9.1. Greenโs Functions -- 9.2. Dynamic Piezoelectric Operator -- 9.3. Fundamental Solutions -- 9.4. Steady-State Solutions -- 9.5. Piezocrystal Waves -- 10: Boundary Element Methods -- 10.1. Boundary Integral Equations -- 10.2. Boundary Element Method -- 10.3. Poisson Equation -- 10.4. Transient Fourier Equation -- 10.5. Laplace Transform BEM -- 10.6. Elastostatic BEM -- 10.7. Fracture Mechanics -- 11: Domain Integrals -- 11.1. Dual Reciprocity Method -- 11.2. Multiple Reciprocity Method -- 11.3. Transient DRM -- 11.4. Transient MRM -- 11.5. Fourier Series Method -- 11.6. Complex Variable BEM -- 12: Finite Deflection of Plates -- 12.1. von Karman Equations -- 12.2. Boundary Integral Equations -- 12.3. Large Deflections -- 12.4. Singularities in Biharmonic Problems -- 13: Miscellaneous Topics -- 13.1. Poroelasticity -- 13.2. Heat Conduction -- 13.3. Thermoelasticity -- 13.4. Neutron Diffusion -- 13.5. Biomechanics -- 14: Quasilinear Elliptic Operators -- 14.1. p-Laplacian -- 14.2. Lane-Emden Equation -- 14.3. Emden-Fowler Equation -- 14.4. Black Hole Solutions -- 14.5. Einstein-Yang-Mills Equation -- Appendix A: Transforms of Distributions -- A.1. Fourier Transform -- A.2. Laplace Transform -- A.3. Inverse Laplace Transform -- Appendix B: Computational Aspects -- Appendix C: List of Differential Operators