The Blow-up Problem for a Semilinear Parabolic Equation with a Potential
نویسندگان
چکیده
Let Ω be a bounded smooth domain in R . We consider the problem ut = ∆u + V (x)u in Ω × [0, T ), with Dirichlet boundary conditions u = 0 on ∂Ω × [0, T ) and initial datum u(x, 0) = Mu0(x) where M ≥ 0, u0 is positive and compatible with the boundary condition. We give estimates for the blow up time of solutions for large values of M . As a consequence of these estimates we find that, for M large, the blow up set concentrates near the points where u 0 V attains its maximum.
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