On a nonuniform parabolic equation with mixed boundary condition

Author:
C. V. Pao

Journal:
Proc. Amer. Math. Soc. **49** (1975), 83-89

MSC:
Primary 35K20

MathSciNet review:
0377286

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Abstract: This paper discusses the existence of weak solutions for an initial boundary-value problem of a nonuniform second order parabolic equation in which the coefficient of is nonnegative and the coefficient matrix of the elliptic part is not necessarily positive definite. When , this problem is reduced to a degenerate elliptic system. A discussion of the existence of weak solutions for the degenerate elliptic boundary-value problem from the parabolic system is included.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0377286-0

Keywords:
Nonuniform parabolic equations,
degenerate elliptic equations,
weak solutions,
initial boundary-value problems

Article copyright:
© Copyright 1975
American Mathematical Society