The parabolic logistic equation with blow-up initial and boundary values
نویسندگان
چکیده
منابع مشابه
The Parabolic Logistic Equation with Blow-up Initial and Boundary Values
In this article, we investigate the parabolic logistic equation with blow-up initial and boundary values over a smooth bounded domain Ω: ( ut −∆u = a(x, t)u− b(x, t)u in Ω× (0, T ), u =∞ on ∂Ω× (0, T ) ∪ Ω× {0}, where T > 0 and p > 1 are constants, a and b are continuous functions, with b > 0 in Ω × [0, T ), b(x, T ) ≡ 0. We study the existence and uniqueness of positive solutions, and their as...
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* Correspondence: zhgs917@163. com Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang 212013, China Full list of author information is available at the end of the article Abstract This article deals with the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary condition. The blow-up and globa...
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where Ω is a bounded domain in RN for N ≥ 1 with C2 boundary ∂Ω, p, q, l and k are positive parameters, the weight function f (x, y) is nonnegative, nontrivial, continuous and defined for x ∈ ∂Ω, y ∈ Ω, while the nonnegative nontrivial initial Received November 14, 2012, accepted January 28, 2013. Communicated by Eiji Yanagida. 2010 Mathematics Subject Classification: 35B35, 35K50, 35K55.
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The purpose of this work is to deal with the blow-up behavior of the nonnegative solution to a degenerate and singular parabolic equation with nonlocal boundary condition. The conditions on the existence and non-existence of the global solution are given. Further, under some suitable hypotheses, we discuss the blow-up set and the uniform blow-up profile of the blow-up solution. c ©2016 All righ...
متن کاملThe Blow–up Rate for a Semilinear Parabolic Equation with a Nonlinear Boundary Condition
In this paper we obtain the blow-up rate for positive solutions of ut = uxx−λu, in (0, 1)×(0, T ) with boundary conditions ux(1, t) = uq(1, t), ux(0, t) = 0. If p < 2q − 1 or p = 2q − 1, 0 < λ < q, we find that the behaviour of u is given by u(1, t) ∼ (T − t) − 1 2(q−1) and, if λ < 0 and p ≥ 2q − 1, the blow up rate is given by u(1, t) ∼ (T − t) − 1 p−1 . We also characterize the blow-up profil...
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2012
ISSN: 0021-7670,1565-8538
DOI: 10.1007/s11854-012-0036-0