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Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions…
We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical reactions models and solid fuel…
We study steady-state thin films on a chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the one-dimensional steady-state solutions that…
In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized…
In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B…
Well-posedness of a reversible variant of the Gray-Scott model is shown, along with the convergence of each trajectory to one of the two spatially homogeneous steady states. The principle of linearized stability provides the local…
It is well known that simple reaction-diffusion systems can display very rich pattern formation behavior. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic…
Doubly diffusive convection is considered in a vertical slot where horizontal temperature and solutal variations provide competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, the…
We analyze the pattern forming ability and pattern stability for a one-dimensional non-linear transport-diffusion equation on the circle. We show that the trivial steady state is stable when diffusion is sufficiently strong. In the limit…
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…
This article offers a review of results for solitons in 2D and 3D models of nonlinear dissipative media. The existence of such solitons requires to maintain two balances: between nonlinear self-focusing and linear diffraction and/or…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
We study the statics and dynamics of a stable, mobile, self-bound three-dimensional dipolar matter-wave droplet created in the presence of a tiny repulsive three-body interaction. In frontal collision with an impact parameter and in angular…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
Following the approach of [E1, M1, M2, S1, S2, SZJV] for reaction diffusion systems, we justify rigorously the Eckhaus stability criterion for stability of convective Turing patterns, as derived formally by complex Ginzburg-Landau…
In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…
In this paper we study a class of stationary states for reaction--diffusion systems of $k\geq 3$ densities having disjoint supports. For a class of segregation states governed by a variational principle we prove existence and provide…
We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surface and are in contact with a solid substrate. The model couples evolution equations for the film height and the local polarization…
Self-diffusion and radial distribution functions are studied in a strongly confined Lennard-Jones fluid. Surprisingly, in the solid-liquid phase transition region, where the system exhibits dynamic coexistence, the self-diffusion constants…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are considered under general assumptions. The existence of stationary solutions with a single internal transition layer in such reaction-diffusion systems is shown using…