Partial Differential Equations of Parabolic Type by Avner Friedman (English) Pap

Publisher Description

This accessible and self-contained treatment provides even readers previously unacquainted with parabolic and elliptic equations with sufficient background to understand research literature. Author Avner Friedman - Director of the Mathematical Biosciences Institute at The Ohio State University - offers a systematic and thorough approach that begins with the main facts of the general theory of second order linear parabolic equations. Subsequent chapters explore asymptotic behavior of solutions, semi-linear equations and free boundary problems, and the extension of results concerning fundamental solutions and the Cauchy problem to systems of parabolic equations. The final chapter concerns questions of existence and uniqueness for the first boundary value problem and the differentiability of solutions, in terms of both elliptic and parabolic equations. The text concludes with an appendix on nonlinear equations and bibliographies of related works.

Author Biography

Avner Friedman is Director of the Mathematical Biosciences Institute at Ohio State University.

Table of Contents

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

Long Description

With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature. Systematic and thorough, it advances from the main facts of the general theory to questions of existence and uniqueness for the first boundary value problem and the differentiability of solutions. 1964 edition.

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