Electron. J. Differential Equations,
Vol. 2017 (2017), No. 171, pp. 1-23.
Asymptotic behavior of solutions to a system of Schrodinger equations
Xavier Carvajal, Pedro Gamboa, Sarka Necasova,
Huy Hoang Nguyen, Octavio Vera
Abstract:
This article concerns the behaviour of solutions to a coupled system
of Schrodinger equations that has applications in many physical
problems, especially in nonlinear optics. In particular, when the solution
exists globally, we obtain the growth of the solutions in the energy space.
Finally, some conditions are also obtained for having blow-up in this space.
Submitted October 24, 2016. Published July 7, 2017.
Math Subject Classifications: 35A07, 35Q53.
Key Words: Coupled Schrodinger system; energy conservation; global solution;
growth of solutions; blow-up; well-posedness.
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Xavier Carvajal
Instituto de Matemática
Universidade Federal do Rio de Janeiro
Brasil
email: carvajal@im.ufrj.br
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Pedro Gamboa
Instituto de Matemática
Universidade Federal do Rio de Janeiro
Brasil
email: pgamboa@im.ufrj.br
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Sárka Necasov'a
Mathematical Institute of the Academy of Sciences
Zitná 25, 115 67 Praha 1
Czech Republic
email: matus@math.cas.cz
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Huy Hoang Nguyen
Instituto de Matemática and Polo de Xerém
Universidade Federal do Rio de Janeiro, Brasil
email: nguyen@im.ufrj.br
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Octavio Vera
Universidad del Bío-Bío
Av. Collao 1202, Casilla 5-C
Concepción, Chile
email: overa@ubiobio.cl, octaviovera49@gmail.com
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