Huashui Zhan, Zhaosheng Feng
We study the evolution p-Laplacian equation with the nonlinear gradient term
where , p>1 and p>q>0. When a(x)>0 and B(x)>0, the uniqueness of weak solution to this equation may not be true. In this study, under the assumptions that the diffusion coefficient a(x) and the damping coefficient B(x) are degenerate on the boundary, we explore not only the existence of weak solution, but also the uniqueness of weak solutions without any boundary value condition.
Submitted April 9, 2017. Published December 31, 2017.
Math Subject Classifications: 35L65, 35K85, 35R35.
Key Words: Evolution p-Laplacian equation; weak solution; uniqueness; boundary value condition.
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| Huashui Zhan |
School of Applied Mathematics
Xiamen University of Technology
Xiamen, Fujian 361024, China
| Zhaosheng Feng |
Department of Mathematics
University of Texas-Rio Grande Valley
Edinburg, TX 78539, USA
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