Existence of solutions to an evolution p-Laplacian equation with a nonlinear gradient term
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Date
2017-12-31
Authors
Zhan, Huashui
Feng, Zhaosheng
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We study the evolution p-Laplacian equation with the nonlinear gradient term
ut = div(α(x)|∇u|p-2∇u) - B(x)|∇u|q,
where α(x), B(x) ∈ C1(Ω̅), p > 1 and p > q > 0. When α(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 α(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.
Description
Keywords
Evolution p-Laplacian equation, Weak solution, Uniqueness, Boundary value condition
Citation
Zhan, H., & Feng, Z. (2017). Existence of solutions to an evolution p-Laplacian equation with a nonlinear gradient term. <i>Electronic Journal of Differential Equations, 2017</i>(311), pp. 1-15.