Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10427215 | Nonlinear Analysis: Theory, Methods & Applications | 2005 | 13 Pages |
Abstract
We study the possible continuation of solutions of a nonlinear parabolic problem after the blow-up time. The nonlinearity in the equation is dissipative and blow-up is caused by the nonlinear boundary condition of the form âu/âν=|u|q-1u, where q>1 is subcritical in H1(Ω). If the dissipative term in the equation is linear then we show that blow-up of positive solutions is complete. If the dissipative term is superlinear then the solution can be continued inside the spatial domain. On the other hand, we find sufficient conditions on the nonlinearities guaranteeing that no reasonable continuation can be expected on the boundary.
Related Topics
Physical Sciences and Engineering
Engineering
Engineering (General)
Authors
Pavol Quittner, AnÃbal RodrÃguez-Bernal,