2026-06-01T01:17:46Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/575082023-08-25T14:21:49Zcom_20.500.14352_14col_20.500.14352_15
On the behavior and cases of nonexistence of the free-boundary in a semibounded porous-medium
Díaz Díaz, Jesús Ildefonso
Kersner, R.
517.954
behavior
free boundary
semibounded porous medium
Cauchy-Dirichlet problem
Fokker-Planck equation
qualitative properties
free boundaries
interfaces
Geometría diferencial
1204.04 Geometría Diferencial
The authors consider the Fokker-Planck equation ut=(um)xx+b(uλ)x, x>0, t>0, with initial and boundary data u(x,0)=u0(x), x>0, u(0,t)=u1(t), t>0, u0 having its support in a bounded interval. They concentrate on the case 0<λ<1, m≥1 with the aim of investigating the behavior of the free boundary, i.e. the moving boundary of suppu, in various different cases. When b>0 it is shown that if u1 tends to zero as t→∞, then the free boundary tends to zero. If u1 vanishes in a finite time, so does the free boundary. The possibility that the free boundary tends to infinity is also discussed. Moreover, conditions are found on m,λ and on u1 such that the free boundary can be estimated from above (localization) and from below by a positive constant. When b<0 it is shown that the free boundary never exists (for λ≥1, m>1 the free boundary is known to start from the right endpoint of suppu0).
CAICYT (Spain)
AKA (Hungary)
Depto. de Análisis Matemático y Matemática Aplicada
Fac. de Ciencias Matemáticas
TRUE
pub
2023-06-20T16:57:22Z
2023-06-20T16:57:22Z
1988-05-15
journal article
https://hdl.handle.net/20.500.14352/57508
0022-247X
10.1016/0022-247X(88)90061-3
eng
restricted access
application/pdf
Elsevier