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.
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