Existence of classical solutions for singular parabolic problems

Authors:
C. Y. Chan and Benedict M. Wong

Journal:
Quart. Appl. Math. **53** (1995), 201-213

MSC:
Primary 35K20; Secondary 35K65

DOI:
https://doi.org/10.1090/qam/1330648

MathSciNet review:
MR1330648

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Abstract | References | Similar Articles | Additional Information

Abstract: Let with a constant less than 1. Its Green's function corresponding to first boundary conditions is constructed by eigenfunction expansion. With this, a representation formula is established to obtain existence of a classical solution for the linear first initial-boundary value problem. Uniqueness of a solution follows from the strong maximum principle. Properties of Green's function and of the solution are also investigated.

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DOI:
https://doi.org/10.1090/qam/1330648

Article copyright:
© Copyright 1995
American Mathematical Society