On uniqueness of large solutions of nonlinear parabolic equations in nonsmooth domains
نویسندگان
چکیده
We study the existence and uniqueness of the positive solutions of the problem (P): ∂tu − ∆u + u q = 0 (q > 1) in Ω × (0,∞), u = ∞ on ∂Ω × (0,∞) and u(., 0) ∈ L(Ω), when Ω is a bounded domain in R . We construct a maximal solution, prove that this maximal solution is a large solution whenever q < N/(N − 2) and it is unique if ∂Ω = ∂Ω c . If ∂Ω has the local graph property, we prove that there exists at most one solution to problem (P). 1991 Mathematics Subject Classification. 35K60, 34.
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