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 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.

Scala, R., Schimperna, G. (2016). On the viscous Cahn-Hilliard equation with singular potential and inertial term. AIMS MATHEMATICS, 1(1), 64-76 [10.3934/Math.2016.1.64].

On the viscous Cahn-Hilliard equation with singular potential and inertial term

Scala, Riccardo;
2016-01-01

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 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.
2016
Scala, R., Schimperna, G. (2016). On the viscous Cahn-Hilliard equation with singular potential and inertial term. AIMS MATHEMATICS, 1(1), 64-76 [10.3934/Math.2016.1.64].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1087426