Initial Boundary Value Problems in Mathematical Physics

ISBN-13: 9783519021025 / Niemiecki / Miękka / 1986 / 266 str.

Rolf Leis

Opis

The lectures presented in this book were given at the University of Bonn in the academic year 1983/4 and in part at the University of Strathclyde, Glasgow. Their aim was to introduce graduate students of both mathematics and physics to the time dependent theory of linear equations of mathematical physics and to classical scattering theory. Using Hilbert space methods, the theory was developed so that the asymptotic behaviour of the solutions for large t could be discussed. The presentation of the theory is made using equations that are of particular interest for the mathematician and the physicist. The wave equation is considered, as are first order systems of linear acoustics and electromagnetism. This is followed by a discussion of a Schrodinger equation with a Coulomb potential, the equations of linear elasticity, the plate equation, and the equations of thermoelasticity. The reader is assumed to have a basic knowledge of functional analysis. However, for convenience, the required background is presented in the second chapter.

Spis treści

1. Introduction.- 2. Linear operators.- 3. The wave equation.- 4. The spectrum of A and boundary value problems.- 5. The free space problem for the wave equation.- 6. The wave equation continued: time-asymptotic behaviour of the solutions.- 7. Linear acoustics.- 8. Maxwell’s equations.- 9. Linear acoustics and Maxwell’s equations continued.- 10. A Schrödinger equation.- 11. Linear elasticity.- 12. The plate equation.- 13. Linear thermoelasticity.- A.1 Proof of Theorem 5.6.- A.2 Proof of Korn’s inequality.- References.- Notation.