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Strong entropy solutions of parabolic-hyperbolic degenerate scalar conservation laws. (Solution forte entropique de lois scalaires hyperboliques-paraboliques dégénérées.) (French) Zbl 0935.35085
Summary: We study a class of degenerate equations \(u_t -\Delta \varphi(u) - \text{div}(\nu(u){\mathbf G})= 0\) associated to the Cauchy-Dirichlet problem. The special feature of the framework is double: the nonlinear equation degenerates into first order hyperbolic type if the unknown value \(u\) is less than a critical value, i.e. on an interval of solution values: we are concerned with the existence, stability and uniqueness of strong entropy solutions under appropriate assumptions on the data.

MSC:
35K65 Degenerate parabolic equations
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
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