Artículo
Exponential decay for a class of non-local non-linear Schrödinger equations with localised damping
Fecha de publicación:
14/09/2022
Editorial:
International Press Boston
Revista:
Communications in Mathematical Sciences
ISSN:
1539-6746
e-ISSN:
1945-0796
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
In this paper we study the exponential decay of both the charge and the free energy for solutions of a family of non-linear, non-local Schrdinger equations with localised damping on the whole line. We first establish an observability inequality for the linear flow, from which we obtain the result in the linear case. Then we consider the non-linear case and by perturbative arguments we obtain the exponential decay for solutions with small initial data. Finally we discuss qualitative aspects of the dynamics and show that the stabilisation rate becomes smaller as the free damping region is chosen around the origin.
Palabras clave:
STABILISATION
,
LOCALISED DAMPING
,
NON LINEAR SCHROEDINGER
,
HARTREE POTENTIAL
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Articulos(INMABB)
Articulos de INST.DE MATEMATICA BAHIA BLANCA (I)
Articulos de INST.DE MATEMATICA BAHIA BLANCA (I)
Citación
de Leo, Mariano Fernando; Exponential decay for a class of non-local non-linear Schrödinger equations with localised damping; International Press Boston; Communications in Mathematical Sciences; 20; 6; 14-9-2022; 1685 – 1701
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