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Uniqueness of entropy solutions for nonlinear degenerate parabolic problems. (English) Zbl 1052.35106

Summary: We consider the general degenerate parabolic equation: \[ u_t-\Delta b(u)+ \text{div}\,F(u)= f\quad\text{in }Q\in]0,t [\times \mathbb{R}^N,\;t>0. \] We prove existence of Kruzkhov entropy solutions of the associated Cauchy problem for bounded data where the flux function \(F\) is supposed to be continuous. Uniqueness is established under some additional assumptions on the modulus of continuity of \(F\) and \(b\).

MSC:

35K65 Degenerate parabolic equations
35L65 Hyperbolic conservation laws
35K15 Initial value problems for second-order parabolic equations
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