Strongly Elliptic Systems and Boundary Integral Equations

ISBN-13: 9780521663328 / Angielski / Twarda / 2000 / 372 str.

William Charles Hector McLean

Opis

Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. William McLean provides the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains. Included are chapters on three specific examples: the Laplace equation, the Helmholtz equation and the equations of linear elasticity. The book affords an ideal background for studying the modern research literature on boundary element methods.

Recenzje

'The author is to be congratulated on successfully establishing a bridge between basic undergraduate material and the modern research literature in boundary element methods … Compliments are due both to the author and also to his numerous associates - duly acknowledged in the preface - for generating a concise and professional presentation of conceptually difficult material.' The Mathematical Gazette

Spis treści

Introduction; 1. Abstract linear equations; 2. Sobolev spaces; 3. Strongly elliptic systems; 4. Homogeneous distributions; 5. Surface potentials; 6. Boundary integral equations; 7. The Laplace equation; 8. The Helmholtz equation; 9. Linear elasticity; Appendix A. Extension operators for Sobolev spaces; Appendix B. Interpolation spaces; Appendix C. Further properties of spherical harmonics; Index of notation; Index.