Related papers: Reaction-diffusion systems of Maxwell-Stefan type …
In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise,…
We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction $A + B \to S$ in a vertical Hele-Shaw cell under constant gravity. We have recently reported that concentration-dependent…
This paper demonstrates a lower and upper solution method to investigate the asymptotic behaviour of the conservative reaction-diffusion systems associated with Markovian process algebra models. In particular, we have proved the uniform…
We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction is expected between the two waves. When restricting to the…
Pattern formation in soft, active, and biological matter is described by two ostensibly distinct continuum frameworks: phase-field theories driven by chemical-potential gradients, and mass-conserving reaction-diffusion (McRD) dynamics…
A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the…
In this paper, we prove global-in-time existence of strong solutions to a class of fractional parabolic reaction-diffusion systems posed in a bounded domain of $\mathbb{R}^N$. The nonlinear reactive terms are assumed to satisfy natural…
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects…
The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…
We establish a weak-strong uniqueness principle for solutions to entropy-dissipating reaction-diffusion equations: As long as a strong solution to the reaction-diffusion equation exists, any weak solution and even any renormalized solution…
Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…
We develop mixed finite element methods for nonlinear reaction-diffusion equations with interfaces which have Robin-type interface conditions. We introduce the velocity of chemicals as new variables and reformulate the governing equations.…
We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of…
Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves…
In a scalar reaction-diffusion equation, it is known that the stability of a steady state can be determined from the Maslov index, a topological invariant that counts the state's critical points. In particular, this implies that pulse…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
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…
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…
Mass-action chemical reaction systems are frequently used in Computational Biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly…
The validity of two fundamental concepts of classical chemical kinetics - the notion of "Chemical Equilibrium" and the "Law of Mass Action" - are re-examined for reversible \textit{diffusion-limited} reactions (DLR), as exemplified here by…