A New Method to Deal with the Stability of the Weak Solutions for a Nonlinear Parabolic Equation
Consider the nonlinear parabolic equation ∂u/∂t-div(a(x)|∇u|p-2∇u)=f(x,t,u,∇u) with axx∈Ω>0 and a(x)x∈∂Ω=0. Though it is well known that the degeneracy of a(x) may cause the usual Dirichlet boundary value condition to be overdetermined, and only a partial boundary value condition is needed, since...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/3070738 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832560749417857024 |
|---|---|
| author | Huashui Zhan |
| author_facet | Huashui Zhan |
| author_sort | Huashui Zhan |
| collection | DOAJ |
| description | Consider the nonlinear parabolic equation ∂u/∂t-div(a(x)|∇u|p-2∇u)=f(x,t,u,∇u) with axx∈Ω>0 and a(x)x∈∂Ω=0. Though it is well known that the degeneracy of a(x) may cause the usual Dirichlet boundary value condition to be overdetermined, and only a partial boundary value condition is needed, since the nonlinearity, this partial boundary can not be depicted out by Fichera function as in the linear case. A new method is introduced in the paper; accordingly, the stability of the weak solutions can be proved independent of the boundary value condition. |
| format | Article |
| id | doaj-art-9e7a36344652492381b33d2c8bbdf0cd |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9e7a36344652492381b33d2c8bbdf0cd2025-02-03T01:26:47ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/30707383070738A New Method to Deal with the Stability of the Weak Solutions for a Nonlinear Parabolic EquationHuashui Zhan0School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaConsider the nonlinear parabolic equation ∂u/∂t-div(a(x)|∇u|p-2∇u)=f(x,t,u,∇u) with axx∈Ω>0 and a(x)x∈∂Ω=0. Though it is well known that the degeneracy of a(x) may cause the usual Dirichlet boundary value condition to be overdetermined, and only a partial boundary value condition is needed, since the nonlinearity, this partial boundary can not be depicted out by Fichera function as in the linear case. A new method is introduced in the paper; accordingly, the stability of the weak solutions can be proved independent of the boundary value condition.http://dx.doi.org/10.1155/2018/3070738 |
| spellingShingle | Huashui Zhan A New Method to Deal with the Stability of the Weak Solutions for a Nonlinear Parabolic Equation Journal of Function Spaces |
| title | A New Method to Deal with the Stability of the Weak Solutions for a Nonlinear Parabolic Equation |
| title_full | A New Method to Deal with the Stability of the Weak Solutions for a Nonlinear Parabolic Equation |
| title_fullStr | A New Method to Deal with the Stability of the Weak Solutions for a Nonlinear Parabolic Equation |
| title_full_unstemmed | A New Method to Deal with the Stability of the Weak Solutions for a Nonlinear Parabolic Equation |
| title_short | A New Method to Deal with the Stability of the Weak Solutions for a Nonlinear Parabolic Equation |
| title_sort | new method to deal with the stability of the weak solutions for a nonlinear parabolic equation |
| url | http://dx.doi.org/10.1155/2018/3070738 |
| work_keys_str_mv | AT huashuizhan anewmethodtodealwiththestabilityoftheweaksolutionsforanonlinearparabolicequation AT huashuizhan newmethodtodealwiththestabilityoftheweaksolutionsforanonlinearparabolicequation |