Unbounded solutions of the nonlocal heat equation
نویسندگان
چکیده
منابع مشابه
Unbounded solutions of the nonlocal heat equation
We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: ut = J ∗u−u , where J is a symmetric continuous probability density. Depending on the tail of J , we give a rather complete picture of the problem in optimal classes of data by: (i) estimating the initial trace of (possibly unbounded) solutions; (ii) showing existence and uniqueness results in a su...
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The initial-boundary value problem for the nonlinear heat equation u, = Au + Xf(u) might possibly have global classical unbounded solutions, u* = u(x, r; uS), for some "critical" initial data u*. The asymptotic behaviour of such solutions is studied, when there exists a unique bounded steady state w(x,A) for some values of L We find, for radial symmetric solutions, that u*(r,t)-*w{r) for any 0 ...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Analysis
سال: 2011
ISSN: 1534-0392
DOI: 10.3934/cpaa.2011.10.1663