Existence and regularity results for doubly nonlinear inclusions with nonmonotone perturbation

This paper deals with a class of nonlinear evolution inclusions arising from enthalpy formulation of heat conduction problems with phase change and nonmonotone source. Using time-discretization technique and monotone operators theory, we show the existence of weak solutions. Then we prove strong convergence of approximate solutions and lift regularity of the weak solutions under appropriate conditions. Moreover, application to physical model described by hemivariational inequality is given.