Zhan, HuashuiFeng, Zhaosheng2022-10-072022-10-072017-12-31Zhan, 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. 1-15.1072-6691https://hdl.handle.net/10877/16198We 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.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalEvolution p-Laplacian equationWeak solutionUniquenessBoundary value conditionArticle