Blow-up set for a semilinear heat equation with small diffusion
نویسندگان
چکیده
منابع مشابه
Initial blow-up solution of a semilinear heat equation
We study the existence and uniqueness of a maximal solution of equation ut − ∆u + f(u) = 0 in Ω× (0,∞), where Ω is a domain with a non-empty compact boundary, which satisfies u = g on ∂Ω × (0,∞), assuming that g and f are given continuous functions and f is also convex, nondecreasing, f(0) = 0 and verifies Keller-Osserman condition. We show that if the boundary of Ω satisfies the parabolic Wien...
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where u is the temperature, d is the diffusion coefficient, and the integral term represents the memory effect in the material. The study of this type of equations has drawn a considerable attention, see [3, 4, 10, 12, 13]. From a mathematical point of view, one would expect the integral term to be dominated by the leading term in the equation. Therefore, the theory of parabolic equations appli...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2010
ISSN: 0022-0396
DOI: 10.1016/j.jde.2010.03.028