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We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition parameter tends to infinity, the system solution converges to…
We study the surface diffusion flow acting on a class of general (non--axisymmetric) perturbations of cylinders $\mathcal{C}_r$ in ${\rm I \! R}^3$. Using tools from parabolic theory on uniformly regular manifolds, and maximal regularity,…
Colloidal particles at fluid interfaces can enhance the stability of drops and bubbles. Yet, their effect on mass transfer in these multiphase systems remains ambiguous, with some experiments reporting strongly hindered diffusion, while…
We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the…
The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. The equations consist of a reaction-diffusion equation for the substrate concentration and a fourth-order Cahn-Hilliard-type equation…
In this paper we consider the Cahn-Hilliard equation endowed with Wentzell boundary condition which is a model of phase separation in a binary mixture contained in a bounded domain with permeable wall. Under the assumption that the…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
We establish short-time existence of a smooth solution to the surface diffusion equation with an elastic term and without an additional curvature regularization in three space dimensions. We also prove the asymptotic stability of strictly…
The diffuse interface model of Cahn-Hilliard-van der Waals is often used to study various aspects of multi-phase flows such as droplets coalescence and contact line dynamics. The original model of Cahn-Hilliard-van der Waals uses an…
The evolution of two isothermal, incompressible, immiscible fluids in a bounded domain is governed by Cahn-Hilliard-Navier-Stokes equations (CHNS System). In this work, we study the well-posedness results for the CHNS system with…
The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with…
This work aims to numerically investigate the linear global instability of long separation bubbles origin from the changes in the adverse pressure gradient inside a laminar flat plate boundary layer disturbed by placing a bluff body with…
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…
We study the "stiff pressure limit" of a nonlinear drift-diffusion equation, where the density is constrained to stay below the maximal value one. The challenge lies in the presence of a drift and the consequent lack of monotonicity in…
We construct a diffuse-interface model of two-phase solidification that quantitatively reproduces the classic free boundary problem on solid-liquid interfaces in the thin-interface limit. Convergence tests and comparisons with boundary…
We derive a thermodynamically consistent model, which describes the time evolution of a two-phase flow in an evolving domain. The movement of the free boundary of the domain is driven by the velocity field of the mixture in the bulk, which…
Linear global instability of the three-dimensional (3-D), spanwise-homogeneous laminar separation bubble (LSB) induced by shock-wave/boundary-layer interaction (SBLI) in a Mach 7 flow of nitrogen over a $30^{\circ}-55^{\circ}$ double wedge…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or…
This paper concerns global existence for arbitrary nonzero surface tension of bubbles in a Hele-Shaw cell that translate in the presence of a pressure gradient. When the cell width to bubble size is sufficiently large, we show that a unique…