Global Existence and Uniqueness of Solutions to Evolution p-Laplacian Systems with Nonlinear Sources (Journal of Partial Differential Equations, 2018)
This paper presents the global existence and uniqueness of the initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms. The authors use skills of inequality estimation and themethod of regularization to construct a sequence of approximation solutions, hence obtain the global existence of solutions to a regularized system. Then the global existence of solutions to the system of evolution p-Laplacian equations is obtained with the application of a standard limiting process. The uniqueness of the solution is proven when the nonlinear terms are local Lipschitz continuous.
Keywords: Global existence; uniqueness; degenerate; p-Laplacian systems