-widths for singularly perturbed problems
Necessary conditions for local and global existence to a reaction-diffusion system with fractional derivatives.
New exact solutions for a reaction-diffusion equation and a quasi-Camassa Holm equation.
New exact solutions of the Brusselator reaction diffusion model using the exp-function method.
Non local reaction-diffusion equations modelling predator-prey coevolution.
In this paper we examine a predator-prey system with a characteristic of the predator subject to mutation. The ultimate equilibrium of the system is found by Maynard-Smith et al. by the so-called ESS (Evolutionary Stable Strategy). Using a system of reaction-diffusion equations with non local terms, we conclude that ESS result for the diffusion coefficient tending to zero, without resorting to any optimization criterion.
Nonlinear evolution equations with exponential nonlinearities: conditional symmetries and exact solutions
New Q-conditional symmetries for a class of reaction-diffusion-convection equations with exponential diffusivities are derived. It is shown that the known results for reaction-diffusion equations with exponential diffusivities follow as particular cases from those obtained here but not vice versa. The symmetries obtained are applied to construct exact solutions of the relevant nonlinear equations. An application of exact solutions to solving a boundary-value problem with constant Dirichlet conditions...
Nonlinear reaction-diffusion models of self-organization and deterministic chaos: theory and possible applications to description of electrical cardiac activity and cardiovascular circulation.
Nonlocal symmetries and generation of solutions for partial differential equations.
Non-negative solutions to fast diffusions.
The purpose of this work is to study the class of non-negative continuous weak solutions of the non-linear evolution equation∂u/∂t = ∆φ(u), x ∈ Rn, 0 < t < T ≤ +∞.
Non-simultaneous blow-up for a reaction-diffusion system with absorption and coupled boundary flux.
Non-simultaneous blow-up for a semilinear parabolic system with nonlinear memory.
Nonuniqueness of implicit lattice Nagumo equation
We consider the implicit discretization of Nagumo equation on finite lattices and show that its variational formulation corresponds in various parameter settings to convex, mountain-pass or saddle-point geometries. Consequently, we are able to derive conditions under which the implicit discretization yields multiple solutions. Interestingly, for certain parameters we show nonuniqueness for arbitrarily small discretization steps. Finally, we provide a simple example showing that the nonuniqueness...
Novel criteria on global robust exponential stability to a class of reaction-diffusion neural networks with delays.
Numerical simulation of the coagulation dynamics of blood.
Numerical Solutions for some Coupled Systems of Nonlinear Boundary Value Problems.
Numerical study of the stopping of aura during migraine
This work is devoted to the study of migraine with aura in the human brain. Following [6], we class migraine as a propagation of a wave of depolarization through the cells. The mathematical model used, based on a reaction-diffusion equation, is briefly presented. The equation is considered in a duct containing a bend, in order to model one of the numerous circumvolutions of the brain. For a wide set of parameters, one can establish the existence...