A decomposition method for a semilinear boundary value problem with a quadratic nonlinearity.
A classical model for three-phase capillary immiscible flows in a porous medium is considered. Capillarity pressure functions are found, with a corresponding diffusion-capillarity tensor being triangular. The model is reduced to a degenerate quasilinear parabolic system. A global existence theorem is proved under some hypotheses on the model data.
In this article we are interested in the following problem: to find a map that satisfieswhere is an open set of and is a compact isotropic set of . We will show an existence theorem under suitable hypotheses on .
In this article we are interested in the following problem: to find a map that satisfies where Ω is an open set of and E is a compact isotropic set of . We will show an existence theorem under suitable hypotheses on φ.
For a two phase incompressible flow we consider a diffuse interface model aimed at addressing the movement of three-phase (fluid-fluid-solid) contact lines. The model consists of the Cahn Hilliard Navier Stokes system with a variant of the Navier slip boundary conditions. We show that this model possesses a natural energy law. For this system, a new numerical technique based on operator splitting and fractional time-stepping is proposed. The method is shown to be unconditionally stable. We present...
We study a singular perturbation problem arising in the scalar two-phase field model. Given a sequence of functions with a uniform bound on the surface energy, assume the Sobolev norms of the associated chemical potential fields are bounded uniformly, where and is the dimension of the domain. We show that the limit interface as tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.