Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity
This paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr¨odinger equation when the nonlinear damping term corresponds to the limit cases of some “saturating non-Kerr law” F(|u|2)u = a "+(|u|2)α u, with a 2 C, " > 0, 2 = (1 − m) and m...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/72649 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/72649 |
| Access Level: | acceso abierto |
| Palabra clave: | 517 517.9 Partial differential equations Stability in context of PDEs NLS equations Análisis matemático Ecuaciones diferenciales 1202 Análisis y Análisis Funcional 1202.07 Ecuaciones en Diferencias |
| Sumario: | This paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr¨odinger equation when the nonlinear damping term corresponds to the limit cases of some “saturating non-Kerr law” F(|u|2)u = a "+(|u|2)α u, with a 2 C, " > 0, 2 = (1 − m) and m 2 [0, 1). Here we consider the sublinear case 0 < m < 1 with a critical damped coefficient: a 2 C is assumed to be in the set D(m) = z 2 C; Im(z) > 0 and 2pmIm(z) = (1−m)Re(z). Among other things, we know that this damping coefficient is critical, for instance, in order to obtain the monotonicity of the associated operator (see the paper by Liskevich and Perel′muter [16] and the more recent study by Cialdea and Maz′ya [14]). The finite time extinction of solutions is proved by a suitable energy method after obtaining appropiate a priori estimates. Most of the results apply to non-necessarily bounded spatial domains. |
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