On a nonuniform parabolic equation with mixed boundary condition
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- Proc. Amer. Math. Soc. 49 (1975), 83-89 Request permission
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.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 49 (1975), 83-89
- MSC: Primary 35K20
- DOI: https://doi.org/10.1090/S0002-9939-1975-0377286-0
- MathSciNet review: 0377286