We consider the Burgers equation and prove a property which seems to have been unobserved until now: there is no limitation on the growth of the nonnegative initial datum u0(x) at infinity when the problem is formulated on unbounded intervals, as, e.g. (0 +∞), and the solution is unique without prescribing its behaviour at infinity. We also consider the associate stationary problem. Finally, some applications to the linear heat equation with boundary conditions of Robin type are also given.
Mostramos una propiedad que parece no haber sido advertida anteriormente para las soluciones de la ecuación de Burgers: no existe ninguna limitación en el crecimiento para el dato inicial u0(x) en el infinito cuando el problema se formula en intervalos no acotados como, por ejemplo, (0, +∞), y la solución es única. Aplicamos este resultado al caso de condiciones de Robin para la ecuación lineal del calor. Consideramos también el problema de Burgers estacionario.
@article{urn:eudml:doc:41013,
title = {New results on the Burgers and the linear heat equations in unbounded domains.},
journal = {RACSAM},
volume = {99},
year = {2005},
pages = {219-225},
mrnumber = {MR2216104},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41013}
}
Díaz, J.I.; González, S. New results on the Burgers and the linear heat equations in unbounded domains.. RACSAM, Tome 99 (2005) pp. 219-225. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41013/