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Strong solutions for \(u_ t=\phi (u)_{xx}-f(t)\psi (u)_ x\). (English) Zbl 0665.35038

Consider the nonlinear parabolic equation \[ (1)\quad u_ t=\phi (u)_{xx}-f(t)\psi (u)_ x\quad on\quad \Omega \subset (0,\infty)\times {\mathbb{R}}. \] This paper establishes a local result for the regularity of generalized solutions for the problem with one or two degeneracies and proves that, under certain conditions all the derivatives involved are functions and the equation (1) is satisfied almost everywhere.
Reviewer: J.H.Tian

MSC:

35K55 Nonlinear parabolic equations
35B60 Continuation and prolongation of solutions to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
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References:

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