Plouvier, Anne On a class of quasilinear degenerate evolution problems. (Sur une classe de problèmes d’évolution quasi linéaires dégénérés.) (French) Zbl 0836.35080 Rev. Mat. Univ. Complutense Madr. 8, No. 1, 197-227 (1995). Summary: We are concerned with the existence, uniqueness and qualitative behaviour of weak solutions to nonlinear conservation laws, of the form \[ {\partial u \over \partial t} - \text{div} \bigl( {\mathcal A} (.,u) \vec \nabla \varphi (u) \bigr) = 0, \quad \varphi (0) = \varphi' (0) = 0,\;\varphi' \geq 0, \] associated with mixed conditions on the parabolic boundary. We establish a global result of existence for initial data in the space \(L^\infty\), when coefficients of \({\mathcal A}\) are Caratheodory functions.Under these assumptions, we prove the global uniqueness with additional informations on the structure of the matrix of absolute permeability \({\mathcal A} (.,.)\). The asymptotic behaviour of the solution and the local hyperbolic character of the degenerate equation are specified. Cited in 3 Documents MSC: 35K65 Degenerate parabolic equations 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:global existence PDFBibTeX XMLCite \textit{A. Plouvier}, Rev. Mat. Univ. Complutense Madr. 8, No. 1, 197--227 (1995; Zbl 0836.35080) Full Text: EuDML