1. Fundamental solutions and the Cauchy problem 2. The maximum principal and some applications 3. The first initial-boundary value problem 4. Derivation of a priori estimates 5. The second initial-boundary value problem 6. Asymptotic behavior of solutions 7. Semi-linear equations. Nonlinear boundary conditions 8. Free boundary problems 9. Fundamental solutions for parabolic systems 10. Boundary value problems for elliptic and parabolic equations of any order Appendix: Nonlinear equations Appendix bibliography Bibliographical remarks Bibliography Index
Avner Friedman is Director of the Mathematical Biosciences Institute at Ohio State University.