相关论文: Group classification of systems of non-linear reac…
A complete description of $Q$-conditional symmetries of reaction-diffusion-convection equation with arbitrary power nonlinearities is finished. It is shown that the results obtained in the first and second parts of this work (see…
A complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It is shown that all the known results for reaction-diffusion equations with power…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multispecies reaction-diffusion equations. We establish results of existence of solution and maximum principle,…
symmetry, group classification, differential invariants, Lie-classical method,infinitesimal criterion method, RDC equation, KPP equation, similarity solutions.
(2+1) dimensional diffusion equation is considered within the framework of equivalence transformations. Generators for the group are obtained and admissible transformations between linear and nonlinear equations are examined. It is shown…
The aim of this work is to study the global existence of solutions for some coupled systems of reaction diffusion which describe the spread within a population of infectious disease. We consider a triangular matrix diffusion and we show…
Extensive work has been done on the group classification of systems of equations in the literature. This paper identifies the gap in the literature which concerns the group classification of systems of two autonomous nonlinear second-order…
We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear…
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…
Q-conditional (nonclassical) symmetries of the known three-component reaction-diffusion system [K. Aoki et al Theor. Pop. Biol. 50(1) (1996)] modeling interaction between farmers and hunter-gatherers are constructed for the first time. A…
Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this Letter we propose a global…
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.…
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…
A symmetry group classification for fourth-order reaction-diffusion equations, allowing for both second-order and fourth-order diffusion terms, is carried out. The fourth order equations are treated, firstly, as systems of second-order…
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…
A system of equations of the reaction-diffusion type is studied in the framework of both the direct and the inverse prolongation structure. We find that this system allows an incomplete prolongation Lie algebra, which is used to find the…
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…
The purpose of this article is to investigate the emergence of cross-diffusion in the time evolution of two slow-fast species in competition. A class of triangular cross-diffusion system is obtained as the singular limit of a fast…
We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence…