Gradient blowup solutions of a semilinear parabolic equation with exponential source
نویسندگان
چکیده
منابع مشابه
Global Existence and Blowup of Solutions for a Parabolic Equation with a Gradient Term
The author discusses the semilinear parabolic equation ut = ∆u+ f(u) + g(u)|∇u|2 with u|∂Ω = 0, u(x, 0) = φ(x). Under suitable assumptions on f and g, he proves that, if 0 ≤ φ ≤ λψ with λ < 1, then the solutions are global, while if φ ≥ λψ with λ > 1, then the solutions blow up in a finite time, where ψ is a positive solution of ∆ψ + f(ψ) + g(ψ)|∇ψ|2 = 0, with ψ|∂Ω = 0. We study the solutions o...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Analysis
سال: 2012
ISSN: 1534-0392
DOI: 10.3934/cpaa.2013.12.269