Modeling the microstructure evolution of a material embedded in device often involves integral boundary conditions. Here we propose modified Nitsche's method to solve Poisson equation with an condition, which is coupled phase-field equations strongly correlated undergoing metal-insulator transitions. Our numerical experiments demonstrate that proposed achieves optimal convergence rate while con...

In this paper we propose two new monotonicity conditions that could serve as sufficient for uniqueness of Nash equilibria in mean field games. study aim unconditional is independent the length time horizon, regularity starting distribution agents, or regularization effect a non-degenerate idiosyncratic noise. Through rich class simple examples show these are not only dichotomy with each other, ...