Asymptotic Behaviour of a Semilinear Elliptic System with a Large Exponent
نویسندگان
چکیده
منابع مشابه
Asymptotic Behaviour of a Semilinear Elliptic System with a Large Exponent
Consider the problem −∆u = v 2 N−2 , v > 0 in Ω, −∆v = u, u > 0 in Ω, u = v = 0 on ∂Ω, where Ω is a bounded convex domain in R , N > 2, with smooth boundary ∂Ω. We study the asymptotic behaviour of the least energy solutions of this system as p → ∞. We show that the solution remain bounded for p large and have one or two peaks away form the boundary. When one peak occurs we characterize its loc...
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We study the semilinear nonlocal equation ut = J∗u− u− u in the whole R . First, we prove the global well-posedness for initial conditions u(x, 0) = u0(x) ∈ L(R ) ∩ L∞(RN ). Next, we obtain the long time behavior of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J : finite time extinction for p < 1, faster than exponential decay for the ...
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ژورنال
عنوان ژورنال: Journal of Dynamics and Differential Equations
سال: 2006
ISSN: 1040-7294,1572-9222
DOI: 10.1007/s10884-006-9045-y