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A uniqueness result for a class of quasilinear parabolic problems. (Un résultat d’unicité pour une classe de problèmes paraboliques quasi-linéaires.) (French) Zbl 0918.35068
Summary: We discuss the question of uniqueness for some quasilinear parabolic problems of the type: \[ {\partial u\over\partial t}- \text{div}({\mathcal A}(\cdot, u)\text{grad}(u))= f(\cdot,t,u)\quad\text{in }{\mathcal D}'(\Omega\times (0,T)); \]
\[ u\in L^2(0,T; V)\cap C([0,T]; L^2(\Omega)),\quad u(\cdot, 0)= u^0(\cdot)\quad\text{in }\Omega,\quad u^0\in L^2(\Omega), \] where \(V= \{u: u\in H^1(\Omega), u|_{\Gamma_0}= 0\}\), \(\Gamma= \partial\Omega= \Gamma_0\cup \Gamma_1\), and where \({\mathcal A}(x,\lambda)\), \(f(x,t,\lambda)\) are Carathéodory functions with suitable continuity moduli.

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
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