# MathSciDoc: An Archive for Mathematician ∫

#### Analysis of PDEsmathscidoc:1702.03004

2017.1
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 $$\int_\Omega u^{2\gamma-\alpha-\beta}\Delta\ua\Delta\ub dx \geq c\int_\Omega|\Delta \ur |^2dx,$$ which seem to be of interest on their own right.
Existence, Nonlinear fourth order parabolic equations, Thin-ﬁlm equation,Quantum drift-diﬀusion model, Functional inequalities.
@inproceedings{jian-guo2017on,