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ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF A QUASILINEAR PARABOLIC EQUATION WITH ROBIN BOUNDARY CONDITION

Abstract : In this paper we study solutions of the quasi-linear para-bolic equations ∂u/∂t − ∆pu = a(x)|u| q−1 u in (0, T) × Ω with Robin boundary condition ∂u/∂ν|∇u| p−2 = b(x)|u| r−1 u in (0, T) × ∂Ω where Ω is a regular bounded domain in R N , N ≥ 3, q > 1, r > 1 and p ≥ 2. Some sufficient conditions on a and b are obtained for those solutions to be bounded or blowing up at a finite time. Next we give the asymptotic behavior of the solution in special cases.
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Michele Grillot, Philippe Grillot. ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF A QUASILINEAR PARABOLIC EQUATION WITH ROBIN BOUNDARY CONDITION. Advances in Differential Equations, Khayyam Publishing, 2012, pp.401-419. ⟨hal-01149958⟩

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