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Global existence and nonexistence of the solution of a forced nonlinear Schrödinger equation (1995)

Guo, Bo-ling ; Wu, Yong-hui

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 36 (1995), S. 3479-3484

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: In this article, we prove that the solution of the forced nonlinear Schrödinger equation (1.1) below for u0∈H1 and Q(t)∈C1 with u0(0)=Q(0) exists globally if and only if ∫T0||Q'(t)||2 dt〈∞. This result positively answers the conjecture of Q. Y. Bu ["On well-posedness of the forced NLS equation,'' Appl. Anal. 46, 219–239 (1992)]. © 1995 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.531335

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Digitale Medien

A Threshold Result for a Non-local Parabolic Equation (1997)

Wu, Yong-hui

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 20 (1997), S. 933-943

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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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