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Transactions of the American Mathematical Society

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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
MathSciNet review: 797062
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Abstract: Let $ \phi $ 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 $ {u_t} = \phi {({u_x})_x}$ with Neumann boundary conditions has at most one smooth solution.

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