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Sur une classe de problèmes paraboliques quasi-linéaires. (French) Zbl 0605.35044
The author handles two related problems. First he proves the unicity of the solution of the Dirichlet problem (and mixed boundary value problem) for a quasilinear parabolic equation in divergence form. In the second part the author considers a quasilinear elliptic boundary value problem in divergence form and proves that the solutions of a singular, parabolic perturbation of this problem converge strongly in \(L^ p\), \(p=1,2\), to the solution of the elliptic problem.
Reviewer: N.Jacob

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35B25 Singular perturbations in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)