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.
On the viscous Cahn-Hilliard equation with singular potential and inertial term
Riccardo Scala;Giulio Schimperna
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
