Volume 26, Issue 1
Global Existence and Uniqueness of Solutions to Evolution p-Laplacian Systems with Nonlinear Sources

Yingjie Wei and Wenjie Gao

10.4208/jpde.v26.n1.1

J. Part. Diff. Eq., 26 (2013), pp. 1-13.

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  • Abstract

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.

  • History

Published online: 2013-03

  • AMS Subject Headings

35A01, 35A02, 35G55

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