Related papers: Group classification of systems of non-linear reac…
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…
Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form…
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…
To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in…
An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is…
A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady…
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…
The propagation of general electronic quantum states provides information of the interaction of molecular systems with external driving fields. These can also offer understandings regarding non-adiabatic quantum phenomena. Well established…
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
Nonlinear systems of the reaction-diffusion type, including Gierer-Meinhardt models of autocatalysis, are studied by using Lie algebras coming from the prolongation structure. The consequences of this analytical approach, as the…
The group classification of variable coefficient quasilinear reaction-diffusion equations $u_t=u_{xx}+h(x)B(u)$ is carried out exhaustively. This became possible due to usage of a conditional equivalence group found in the course of the…
This article complements recent results of the papers [J. Math. Phys. 41 (2000), 480; 45 (2004), 336] on the symmetry classification of second-order ordinary difference equations and meshes, as well as the Lagrangian formalism and…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
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 authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are…
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…
A class of generalized nonlinear Kolmogorov equations is investigated. We present the group classification of Lie symmetries of the class with respect to the group of equivalence transformations. We find a number of exact solutions of…
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…