## 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

### Keywords:

Kruzkhov entropy solutions; bounded data
Full Text: