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

Jian-Guo Liu Department of Physics and Department of Mathematics, Duke University Xiangsheng Xu Department of Mathematics and Statistics, Mississippi State University

Analysis of PDEs mathscidoc: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.
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@inproceedings{jian-guo2017on,
  title={On a Class of Functional Inequalities and their Applications to Fourth-Order Nonlinear Parabolic Equations},
  author={Jian-Guo Liu, and Xiangsheng Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170206110754228818184},
  year={2017},
}
Jian-Guo Liu, and Xiangsheng Xu. On a Class of Functional Inequalities and their Applications to Fourth-Order Nonlinear Parabolic Equations. 2017. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170206110754228818184.
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