Fundamental Solutions for Differential Operators and Applications

1. Front Matter

   Pages i-xxiii

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2. Introduction

   • Prem K. Kythe

   Pages 1-10

3. Some Basic Concepts

   • Prem K. Kythe

   Pages 11-36

4. Linear Elliptic Operators

   • Prem K. Kythe

   Pages 37-59

5. Linear Parabolic Operators

   • Prem K. Kythe

   Pages 60-84

6. Linear Hyperbolic Operators

   • Prem K. Kythe

   Pages 85-116

7. Nonlinear Operators

   • Prem K. Kythe

   Pages 117-137

8. Elastostatics

   • Prem K. Kythe

   Pages 138-161

9. Elastodynamics

   • Prem K. Kythe

   Pages 162-179

10. Fluid Dynamics

    • Prem K. Kythe

    Pages 180-206

11. Piezoelectrics

    • Prem K. Kythe

    Pages 207-230

12. Boundary Element Methods

    • Prem K. Kythe

    Pages 231-265

13. Domain Integrals

    • Prem K. Kythe

    Pages 266-291

14. Finite Deflection of Plates

    • Prem K. Kythe

    Pages 292-306

15. Miscellaneous Topics

    • Prem K. Kythe

    Pages 307-337

16. Quasilinear Elliptic Operators

    • Prem K. Kythe

    Pages 338-363

17. Back Matter

    Pages 364-414

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Overview Many problems in mathematical physics and applied mathematics can be reduced to boundary value problems for differential, and in some cases, inte­ grodifferential equations. These equations are solved by using methods from the theory of ordinary and partial differential equations, variational calculus, operational calculus, function theory, functional analysis, probability theory, numerical analysis and computational techniques. Mathematical models of quantum physics require new areas such as generalized functions, theory of distributions, functions of several complex variables, and topological and al­ gebraic methods. The main purpose of this book is to provide a self contained and system­ atic introduction to just one aspect of analysis which deals with the theory of fundamental solutions for differential operators and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related applicable and computational features. The sub­ ject matter of this book has its own deep rooted theoretical importance since it is related to Green's functions which are associated with most boundary value problems. The application of fundamental solutions to a recently devel­ oped area of boundary element methods has provided a distinct advantage in that an integral equation representation of a boundary value problem is often x PREFACE more easily solved by numerical methods than a differential equation with specified boundary and initial conditions. This situation makes the subject more attractive to those whose interest is primarily in numerical methods.

• Applications
• Applied Mathematics
• Boundary value problem
• Derivation
• Equations
• Finite
• Identity
• Variable
• biomechanics
• calculus
• development
• equation
• function
• mechanics
• plasticity
• partial differential equations

"Kythe explores fundamental solutions of both linear and nonlinear differential operators from mathematical physics, elasticity, fluid dynamics, piezoelectrics, and cosmology. The book begins with a historical development of the subject.... Three appendices provide background on Fourier and Laplace transforms, details about several computer programs that can be used in conjunction with the book, and a listing of 76 differential operators. Extensive bibliography."   —Choice

• Department of Mathematics, University of New Orleans, New Orleans, USA

  Prem K. Kythe

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