Related papers: Global existence, uniqueness and stability for non…
Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the global existence and boundedness of solutions in all dimensions.…
We prove that the steady state of a class of multidimensional reaction-diffusion systems is asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, and pay particular attention to a special…
We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially…
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…
Understanding the non-equilibrium dynamics of quantum many-body systems remains one of the grand challenges of modern physics. In particular, increasing attention has been devoted to the emergence of non-equilibrium universality classes…
Surface nanobubbles are complex micro- and nanoscale fluid systems. While thermodynamics is believed to dominate nanobubble dynamics, the precise mechanism by which nanobubble evolution is driven by thermodynamics remains unclear. It is…
We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions. Under reasonable hypotheses, we establish the existence of component wise…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
In these notes we discuss recent developments in the field of non-equilibrium quantum dynamics. Specifically, we consider nearly coherent Bose gases brought far out of equilibrium and study their behaviour in view of connections between…
In this paper, we'll show the robustness of global stability for perturbed dissipative dynamical systems.
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
Coupling between chemical fuel consumption and phase separation can lead to condensation at a nonequilibrium steady state, resulting in phase behaviors that are not described by equilibrium thermodynamics. Theoretical models of such…
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…
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 analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…
Diverse physical systems are characterized by their response to small perturbations. Near thermodynamic equilibrium, the fluctuation-dissipation theorem provides a powerful theoretical and experimental tool to determine the nature of…
In this paper we study the local instability to the boundary equilibria and the local stability to the positive equilibria for some chemical reaction-diffusion systems. We first analyze a three-species system with boundary equilibria in…