Maliki, Mohamed; Touré, Hamidou Uniqueness of entropy solutions for nonlinear degenerate parabolic problems. (English) Zbl 1052.35106 J. Evol. Equ. 3, No. 4, 603-622 (2003). 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 \(b\). Cited in 21 Documents MSC: 35K65 Degenerate parabolic equations 35L65 Hyperbolic conservation laws 35K15 Initial value problems for second-order parabolic equations Keywords:Kruzkhov entropy solutions; bounded data PDFBibTeX XMLCite \textit{M. Maliki} and \textit{H. Touré}, J. Evol. Equ. 3, No. 4, 603--622 (2003; Zbl 1052.35106) Full Text: DOI