Related papers: Global existence, uniqueness and stability for non…
The nonequilibrium process in dislocation dynamics and its relaxation to the metastable transition profile is crucial for understanding the plastic deformation caused by line defects in materials. In this paper, we consider the full…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
We prove a global existence, uniqueness and regularity result for a two-species reaction-diffusion volume-surface system that includes nonlinear bulk diffusion and nonlinear (weak) cross diffusion on the active surface. A key feature is a…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear…
The methods of non-equilibrium thermodynamics of systems with an interface have been applied to the study of transport processes in semiconductor junctions. A complete phenomenological model for drift-diffusion processes in a junction has…
We introduce an extension of the concept of renormalised solutions for entropy-dissipating reaction-diffusion systems due to J. Fischer (Arch. Ration. Mech. Anal. 218, 2015) to systems coupled by nonlinear interface conditions. For this…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
This article presents a new phase-field formulation for non-equilibrium interface conditions in rapid phase transformations. With a particular way of defining concentration fields, the classical sharp and diffuse (thick) interface theories…
We examine a thermodynamically consistent diffuse interface model for bulk-surface viscous fluid mixtures. This model consists of a Navier--Stokes--Cahn--Hilliard model in the bulk coupled to a surface Navier--Stokes--Cahn--Hilliard system…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
The influence of nonequilibrium bulk conditions on the properties of the interfaces exhibited by a kinetic Ising--like model system with nonequilibrium steady states is studied. The system is maintained out of equilibrium by perturbing the…
In equilibrium systems with short-ranged interactions, the relative stability of different thermodynamic states generally does not depend on system size (as long as this size is larger than the interaction range). Here, we use a large…
We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially…
In this work we study global well-posedness and large time behaviour for a typical reaction--diffusion system, which include degenerate diffusion, and whose non-linearities arise from chemical reactions. We show that there is an {\it…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the…
A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially…