Research on evolution equations involving nonlinear Laplace operators

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Sufficient conditions for the existence of local (in time) solutions of some evolution equations involving p-Laplace operators are obtained. Moreover, the well-posedness of some evolution equation involving the infinity-Laplace operator is proved, and furthermore, the asymptotic behaviors (e.g., decay rates) of solutions are also revealed. Finally, a couple of effective methods are established in order to construct solutions and analyze their large-time behaviors for evolution equations involving nonlinear Laplace operators through this research project.