Asymptotic behaviour of solutions of quasilinear parabolic equation with Robin boundary condition
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چکیده
In this paper we study solutions of the quasi-linear parabolic equations ∂u/∂t −∆pu = a(x)|u|q−1u in (0, T ) × Ω with Robin boundary condition ∂u/∂ν|∇u|p−2 = b(x)|u|r−1u in (0, T ) × ∂Ω where Ω is a regular bounded domain in IRN , 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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تاریخ انتشار 2011