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On a class of parabolic equations with nonlocal boundary conditions
- Source :
-
Journal of Mathematical Analysis & Applications . Jun2004, Vol. 294 Issue 2, p712-728. 17p. - Publication Year :
- 2004
-
Abstract
- In this paper we study a class of parabolic equations subject to a nonlocal boundary condition. The problem is a generalized model for a theory of ion-diffusion in channels. By using energy method, we first derive some a priori estimates for solutions and then prove that the problem has a unique global solution. Moreover, under some assumptions on the nonlinear boundary condition, it is shown that the solution blows up in finite time. Finally, the long-time behavior of solution to a linear problem is also studied in the paper. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 294
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 13236109
- Full Text :
- https://doi.org/10.1016/j.jmaa.2004.03.021