Abstract
We consider the general degenerate parabolic equation:
\( u_t - \Delta b(u) + div F(u) = f \quad \mathrm{in} \quad Q \in ]0, T [\times \mathbb{R}^N, T > 0 \)
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.
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Maliki, M., Touré, H. Uniqueness of entropy solutions for nonlinear degenerate parabolic problems. J.evol.equ. 3, 603–622 (2003). https://doi.org/10.1007/s00028-003-0105-z
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DOI: https://doi.org/10.1007/s00028-003-0105-z