Elliptic-Parabolic Quasi-Variational Evolution Equations

抄録

We introduce a class of abstract doubly nonlinear evolution equations associated with subdifferential operators depending on the unknown. This is modeled on quasi-variational inequalities for systems of elliptic-parabolic partial differential equations that arise from the flows of multi-component fluids in partially saturated porous media. We prove the existence of a solution by employing the theory of time-dependent subdifferential evolution equations and its generalization. Application examples are given for models of fluid flows and population diffusion with a temperature-dependent constraint.