Remarks on the blow-up rate for critical nonlinear Schrödinger equation with harmonic potential

The existence of global weak solutions to the Cauchy problem for a generalized Camassa-Holm equation with a dissipative term is investigated in the spaceC([0,∞)×R)∩L∞([0,∞);H1(R))provided that its initial valueu0(x)belongs to the spaceH1(R). A one-sided super bound estimate and a space-time higher-norm estimate on the first-order derivatives of the solution with respect to the space variable are derived.

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Entire Blow-Up Solutions of Semilinear Elliptic Systems with Quadratic Gradient Terms

Yue

Zhang

2012

Abstract and Applied Analysis

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We study the existence of entire positive solutions for the semilinear elliptic system with quadratic gradient terms,Δui+|∇ui|2=pi(|x|)fi(u1,u2,…,ud)fori=1,2,…,donRN,N≥3andd∈{1,2,3,…}. We establish the conditions onpithat ensure the existence of nonnegative radial solutions blowing up at infinity and also the conditions for bounded solutions on the entire space. The condition onfiis simple and different to the Keller-Osserman condition.

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Remarks on the blow-up rate for critical nonlinear Schrödinger equation with harmonic potential

Cited by 3 publications

References 17 publications

On the Study of Local Solutions for a Generalized Camassa-Holm Equation

On the Study of Local Solutions for a Generalized Camassa-Holm Equation

TheH1(R)Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation

Entire Blow-Up Solutions of Semilinear Elliptic Systems with Quadratic Gradient Terms

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