Related papers: Global existence, uniqueness and stability for non…
Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. The work is a natural continuation of our paper (Cherniha and Davydovych, 2012)…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…
We study the global existence of classical solutions to volume-surface reaction-diffusion systems with control of mass. Such systems appear naturally from modeling evolution of concentrations or densities appearing both in a volume domain…
The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward…
We investigate dynamics near Turing patterns in reaction-diffusion systems posed on the real line. Linear analysis predicts diffusive decay of small perturbations. We construct a "normal form" coordinate system near such Turing patterns…
This short review covers a wide selection of topics from a multidisciplinary area of dynamics of nonequilibrium systems in physics, chemistry, biology. Theoretical models of colloid particle and protein deposition and adhesion at surfaces,…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
We consider the effective surface motion of a particle that freely diffuses in the bulk and intermittently binds to that surface. From an exact approach we derive various regimes of the effective surface motion characterized by physical…
We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems'', e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in…
We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by…
From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is…
Topological insulating phases are usually found in periodic lattices stemming from collective resonant effects, and it may thus be expected that similar features may be prohibited in thermal diffusion, given its purely dissipative and…
The time-dependent structure, interfacial tension, and evaporation of an oversaturated colloid-rich (liquid) phase in contact with an undersaturated colloid-poor (vapor) phase of a colloidal dispersion is investigated theoretically during…
Mass-conserving reaction-diffusion (MCRD) systems are widely used to model phase separation and pattern formation in cell polarity, biomolecular condensates, and ecological systems. Numerical simulations and formal asymptotic analysis…
Van der Waals interactions are ubiquitous and they play an important role for the stability of materials. Current understanding of this type of coupling is based on linear response theory, while optical nonlinearities are rarely considered…
We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of…
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the…
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…