Mixed problem for a cubic Schrödinger evolution equation with a cubic dissipative term

DOI10.1134/S0001434614090260zbMath1315.35208OpenAlexW2059774826MaRDI QIDQ2343891

Yanyan Li

Publication date: 11 May 2015

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434614090260

zbMATH Keywords

Cauchy-Bunyakovsky inequalityGagliardo-Nirenberg-Sobolev inequalitySchrödinger evolution equation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Time-dependent Schrödinger equations and Dirac equations (35Q41) Strong solutions to PDEs (35D35)

Cites Work

• Uniqueness of positive radial solutions of \(\Delta u+f(u)=0\) in \({\mathbb{R}}^ n\)
• On the cubic evolution Schrödinger equation with a cubic dissipative term: \(iu_t+ i\beta|u|^2u= \Delta u+ \alpha|u|^2u\)
• SOLVABILITY OF A MIXED PROBLEM FOR THE NONLINEAR SCHRÖDINGER EQUATION
• Nonlinear Schrödinger evolution equations
• Uniqueness of solutions of semilinear Poisson equations
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