Editor's statement; Foreword Felix E. Browder; Preface; Preliminaries; 1. Introduction; 2. The Cauchy problem; 3. The initial
value problem; 4. The initial
boundary
value problem for the quarter plane with temperature
boundary specification; 5. The initial
boundary
value problem for the quarter plane with heat
flux
boundary specification; 6. The initial
boundary
value problem for the semi
infinite strip with temperature
boundary specification and heat
flux
boundary specification; 7. The reduction of some initial
boundary
value problems for the semi
infinite strip, to integral equations: some exercises; 8. Integral equations; 9. Solutions of boundary
value problems for all times and periodic solutions; 10. Analyticity of solutions; 11. Continuous dependence upon the data for some state
estimation problems; 12. Some numerical methods for some state
estimation problems; 13. Determination of an unknown time
dependent diffusivity a(t) from overspecified data; 14. Initial
and/or boundary
value problems for gneral regions with Hölder continuous boundaries; 15. Some properties of solutions in general domains; 16. The solution in a general region with temperature
boundary specification: the method of perron
poincaré; 17. The one
phase stefan problem with temperature
boundary specification; 18. The one
phase stefan problem with flux
boundary specification: some exercises; 19. The inhomogeneous heat equation ut=uxx+f(x,t); 20. An application of the inhomogeneous heat equation: the equation ut=uxx+f(x,t,u,ux); Symbol index; Subject index.
