Related papers: Doubly Degenerate Diffuse Interface Models of Surf…
In this paper we study the Cauchy problem for doubly dissipative elastic waves in two space dimensions, where the damping terms consist of two different friction or structural damping. We derive energy estimates and diffusion phenomena with…
In this paper, we derive a dynamic surface elasticity model for the two-dimensional midsurface of a thin, three-dimensional, homogeneous, isotropic, nonlinear gradient elastic plate of thickness $h$. The resulting model is parameterized by…
We minimized the interface diffuseness in the phase-field models by introducing the parabolic double-well potential and localizing the solute redistribution (or latent heat release) into a narrow region within the phase-field interface. In…
A diffused-interface approach based on the Allen-Cahn phase field equation is developed within a high-order Discontinuous Galerkin framework. The interface capturing technique is based on the balance between explicit diffusion and…
We prove the short-time asymptotic formula for the interfaces and local solutions near the interfaces for the nonlinear double degenerate reaction-diffusion equation of turbulent filtration with fast diffusion and strong absorption \[…
In this paper, we study an optimal control problem for a coupled non-linear system of reaction-diffusion equations with degenerate diffusion, consisting of two partial differential equations representing the density of cells and the…
In the present work, we propose an advection-diffusion equation with Hausdorff deformed derivatives to stud the turbulent diffusion of contaminants in the atmosphere. We compare the performance of our model to fit experimental data against…
We consider the dynamics and kinetic roughening of wetting fronts in the case of forced wetting driven by a constant mass flux into a 2D disordered medium. We employ a coarse-grained phase field model with local conservation of density,…
We find analytical solutions to the Cahn-Hilliard equation for the dynamics of an interface in a system with a conserved order parameter (Model B). We show that, although steady-state solutions of Model B are unphysical in the far-field,…
The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding…
The idea of working with a near-critical phase-separated liquid mixture whereby the surface tension becomes weak, has recently made the field of laser manipulation of liquid interfaces a much more convenient tool in practice. The…
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
We present new extensions to a method for constructing several families of solvable one-dimensional time-homogeneous diffusions whose transition densities are obtainable in analytically closed-form. Our approach is based on a dual…
A novel numerical strategy is introduced for computing approximations of solutions to a Cahn-Hilliard model with degenerate mobilities. This model has recently been introduced as a second-order phase-field approximation for surface…
The existence of global weak solutions to a parabolic energy-transport system in a bounded domain with no-flux boundary conditions is proved. The model can be derived in the diffusion limit from a kinetic equation with a linear collision…
In many interfacial flow systems, variations of surface properties lead to novel and interesting behaviors. In this work a three-dimensional model of flow dynamics for multicomponent vesicles is presented. The surface composition is modeled…
We study the asymptotic limit of the Cahn-Hilliard equation on an evolving surface with prescribed velocity. The method of formally matched asymptotic expansions is extended to account for the movement of the domain. We consider various…
We propose and analyze a simple variational model for dislocations at semi-coherent interfaces. The energy functional describes the competition between two terms: a surface energy induced by dislocations that compensate the lattice misfit…
In this work, a thermodynamically consistent and conservative diffuse-interface model for gas-liquid-solid multiphase flows is proposed. In this model, a novel free energy for the gas-liquid-solid multiphase flows is established according…
The generalized Allen-Cahn equation, \[ u_t=\varepsilon^2(D(u)u_x)_x-\frac{\varepsilon^2}2D'(u)u_x^2-F'(u), \] with nonlinear diffusion, $D = D(u)$, and potential, $F = F(u)$, of the form \[ D(u) = |1-u^2|^{m}, \quad \text{or} \quad D(u) =…