Related papers: Reaction-Diffusion models: From Particle Systems t…
The spatially distributed reaction networks are indispensable for the understanding of many important phenomena concerning the development of organisms, coordinated cell behavior, and pattern formation. The purpose of this brief discussion…
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)…
We establish the existence of solutions to a class of non-linear stochastic differential equation of reaction-diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained…
Q-conditional symmetries (nonclassical symmetries) for the general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first…
We obtain classification, solvability and nonexistence theorems for positive stationary states of reaction-diffusion and Schr\"odinger systems involving a balance between repulsive and attractive terms. This class of systems contains PDE…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
THis work is a survey of a few nonlinear PDE based models in image restoring.
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…
This paper concerns a general class of PDE-ODE reaction-diffusion systems, which features a singular fast-reaction limit towards a reaction-diffusion equation coupled to a scalar hysteresis operator. As prototypical application, we present…
Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion…
This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains. Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems. Their long-time behaviour is strongly…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
A wide range of new Q-conditional symmetries for reaction-diffusion systems with power diffusivities are constructed. The relevant non-Lie ansatze to reduce the reaction-diffusion systems to ODE systems and examples of exact solutions are…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
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…
We present new results of existence of global solutions for a class of reaction cross-diffusion systems of two equations presenting a cross-diffusion term in the first equation, and possibly presenting a self-diffusion term in any (or both)…
The primary goal of this paper is to characterize solutions to coupled reaction-diffusion systems. Indeed, we use operators theory to show that under suitable assumptions, then the solutions to the reaction-diffusion equations exist. As…
Inspired by a PDE-ODE system of aggregation developed in the biomathematical literature, an interacting particle system representing aggregation at the level of individuals is investigated. It is proved that the empirical density of the…
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…
One-dimensional reaction-diffusion systems are mapped through a similarity transformation onto integrable (and a priori non-stochastic) quantum chains. Time-dependent properties of these chemical models can then be found exactly. The…