Uniqueness for a forward backward diffusion equation

Author:
Alan V. Lair

Journal:
Trans. Amer. Math. Soc. **291** (1985), 311-317

MSC:
Primary 35K55; Secondary 35K65

DOI:
https://doi.org/10.1090/S0002-9947-1985-0797062-5

MathSciNet review:
797062

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Abstract: Let be continuous, have at most finitely many local extrema on any bounded interval, be twice continuously differentiable on any closed interval on which there is no local extremum and be strictly decreasing on any closed interval on which it is decreasing. We show that the initial-boundary value problem for with Neumann boundary conditions has at most one smooth solution.

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0797062-5

Article copyright:
© Copyright 1985
American Mathematical Society