Phenomena of Blowup and Global Existence of the Solution to a Nonlinear Schrödinger Equation

Xiaowei An, Desheng Li and Xianfa Song

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We consider the following Cauchy problem: −iut = Δu − V(x)u + f(x, |u|2)u + (W(x)⋆|u|2)u, x ∈ ℝN, t > 0, u(x, 0) = u0(x), x ∈ ℝN, where V(x) and W(x) are real‐valued potentials and V(x) ≥ 0 and W(x) is even, f(x, |u|2) is measurable in x and continuous in |u|2, and u0(x) is a complex‐valued function of x. We obtain some sufficient conditions and establish two sharp thresholds for the blowup and global existence of the solution to the problem.

Date: 2013
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https://doi.org/10.1155/2013/238410

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:238410

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