Preprint

Inserted: 19 apr 2016
Last Updated: 19 apr 2016

Year: 2016

Abstract:

We consider a relaxation of the viscous Cahn-Hilliard equation induced by the second-order inertial term~$u_{tt}$. The equation also contains a semilinear term $f(u)$ of ``singular'' type. Namely, the function $f$ is defined only on a bounded interval of $\mathbb R$ corresponding to the physically admissible values of the unknown $u$, and diverges as $u$ approaches the extrema of that interval. In view of its interaction with the inertial term $u_{tt}$, the term $f(u)$ is difficult to be treated mathematically. Based on an approach originally devised for the strongly damped wave equation, we propose a suitable concept of weak solution based on duality methods and prove an existence result.

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