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arXiv · 1612.03508

A Class of Functional Inequalities and their Applications to Fourth-Order Nonlinear Parabolic Equations

Jian-Guo Liu·Xiangsheng Xu
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Abstract

We study a class of fourth order nonlinear parabolic equations which include the thin-film equation and the quantum drift-diffusion model as special cases. We investigate these equations by first developing functional inequalities of the type $ \int_\Omega u^{2\gamma-\alpha-\beta}\Delta u^\alpha\Delta u^\beta dx \geq c\int_\Omega|\Delta u^\gamma |^2dx $, which seem to be of interest on their own right.

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Jian-Guo Liu, Xiangsheng Xu. 2016-12-12. A Class of Functional Inequalities and their Applications to Fourth-Order Nonlinear Parabolic Equations. https://arxiv.org/abs/1612.03508

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