A new kind of the solutions of a convection-diffusion equation related to the p(x)-Laplacian

作者：Zhan, Huashui^*

来源：Boundary Value Problems, 2017, 2017(1): 117.

DOI：10.1186/s13661-017-0848-z

• convection-diffusion equation
• p(x)-Laplacian
• stability

A new kind of the solutions of the convection-diffusion equation related to the p(x)-Laplacian is introduced. The equation is degenerate on the boundary, accordingly, the usual boundary value condition cannot be imposed in Dirichlet's way. The test function chosen to verify the uniqueness of the solutions should be independent of the boundary value condition. By the new definition, one can study the stability of the weak solutions without any boundary value condition. The main results of the paper show that the usual homogeneous boundary value condition can be replaced by the degeneracy of the diffusion coefficient and the degeneracy of the convection term on the boundary.

• 出版日期2017-8-18
• 单位厦门理工学院