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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 $ b(t,x)$ of $ {u_t}$ is nonnegative and the coefficient matrix $ ({a_{ij}}(t,x))$ of the elliptic part is not necessarily positive definite. When $ b(t,x) \equiv 0$, 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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Keywords: Nonuniform parabolic equations, degenerate elliptic equations, weak solutions, initial boundary-value problems
Article copyright: © Copyright 1975 American Mathematical Society