Classification of blowup solutions for a parabolic p-Laplacian equation with nonlinear gradient terms

We mainly consider the following degenerate (p>2)(p>2) parabolic equationut−Δpu=λum+μ|∇u|qut−Δpu=λum+μ|∇u|q with homogeneous Dirichlet boundary condition in a bounded domain Ω⊂RNΩ⊂RN. Before studying the properties of the solutions of this equation, we first establish the local-in-time existence of its weak solutions. Then, in different ranges of reaction exponents, we give the complete classification of blowup results including L∞L∞ blowup and gradient blowup. Moreover, under the subcritical condition of q≤p−1q≤p−1, m≤p−1m≤p−1, we can also prove that the solution is global in time.