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 | |
Pedro Gamboa Instituto de Matemática Universidade Federal do Rio de Janeiro Brasil email: pgamboa@im.ufrj.br | |
Sárka Necasov'a Mathematical Institute of the Academy of Sciences Zitná 25, 115 67 Praha 1 Czech Republic email: matus@math.cas.cz | |
Huy Hoang Nguyen Instituto de Matemática and Polo de Xerém Universidade Federal do Rio de Janeiro, Brasil email: nguyen@im.ufrj.br | |
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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