ISSN:
0170-4214
Schlagwort(e):
Engineering
;
Numerical Methods and Modeling
Quelle:
Wiley InterScience Backfile Collection 1832-2000
Thema:
Mathematik
Notizen:
In this paper, we consider the Cauchy problem:(ECP)ut-Δu+p(x)u=u(x,t)∫∝3u2(y,t)/∣x-y∣dy; x∊∝3, t〉0,u(x, 0)=u0(x)≥0 x∊∝3, (0.2)The stationary problem for (ECP) is the famous Choquard-Pekar problem, and it has a unique positive solution ū(x) as long as p(x) is radial, continuous in ∝3, p(x)≥ā〉0, and lim∣x∣→∞p(x)=p¯〉0. In this paper, we prove that if the initial data 0≤u0(x)≤(≢)ū(x), then the corresponding solution u(x, t) exists globally and it tends to the zero steady-state solution as t→∞, if u0(x)≥(≢)ū(x), then the solution u(x,t) blows up in finite time. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
Materialart:
Digitale Medien
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