Related papers: On global dynamics of reaction--diffusion systems …
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
Dynamical systems driven by a general L\'evy stable noise are considered. The inertia is included and the noise, represented by a generalised Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive…
The motto of this paper is: Let's face Bose-Einstein condensation through nonlinear dynamics. We do this by choosing variational forms of the condensate wave functions (of given symmetry classes), which convert the Bose-Einstein condensates…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
The paper deals with local well-posedness, global existence and blow-up results for reaction--diffusion equations coupled with nonlinear dynamical boundary conditions.
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…
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…
Global diffusion of Hamiltonian dynamical systems is investigated by using a coupled standard maps. Arnold web is visualized in the frequency space, using local rotation numbers, while Arnold diffusion and resonance overlaps are…
The mass-based Maxwell-Stefan approach to one-phase multicomponent reactive mixtures is mathematically analyzed. It is shown that the resulting quasilinear, strongly coupled reaction-diffusion system is locally well-posed in an…
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…
An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive,…
Reactive Rayleigh-Taylor systems are characterized by the competition between the growth of the instability and the rate of reaction between cold (heavy) and hot (light) phases. We present results from state-of-the-art numerical simulations…
Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant…
The global stability of the nonhomogeneous positive steady state solution to a diffusive Holling-Tanner predator-prey model in a heterogeneous environment is proved by using a newly constructed Lyapunov function and estimates of nonconstant…
Reaction-diffusion systems with mass dissipation are known to possess blow-up solutions in high dimensions when the nonlinearities have super quadratic growth rates. In dimension one, it has been shown recently that one can have global…
This paper establishes a rigorous mathematical framework for the Multi-Scale Negative Coupled System (MNCS), a dynamical model describing hierarchical state spaces with directed, sign-structured interactions. We address the stabilization of…
We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a continuation method which leads to…
The formalism of linear response theory can be extended to encompass physical situations where an open quantum system evolves towards a non-equilibrium steady-state. Here, we use the framework put forward by Konopik and Lutz [Phys. Rev.…
The use of reaction-diffusion models rests on the key assumption that the underlying diffusive process is Gaussian. However, a growing number of studies have pointed out the prevalence of anomalous diffusion, and there is a need to…
The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species is proved. The equations can be derived from an on-lattice random-walk model with general transition…