Related papers: Traveling waves in reaction-diffusion-convection e…
The present paper is devoted to the study of stability, uniqueness and recurrence of generalized traveling waves of reaction-diffusion equations in time heterogeneous media of ignition type, whose existence has been proven by the authors of…
This paper is concerned with the traveling waves of delayed reaction-diffusion systems where the reaction function possesses the mixed quasimonotonicity property. By the so-called monotone iteration scheme and Schauder's fixed point…
Scalar conservation laws with non-convex fluxes have shock wave solutions that violate the Lax entropy condition. In this paper, such solutions are selected by showing that some of them have corresponding traveling waves for the equation…
Some classes of the so called "travelling wave" solutions of Einstein and Einstein - Maxwell equations in General Relativity and of dynamical equations for massless bosonic fields in string gravity in four and higher dimensions are…
We consider a single component reaction-diffusion equation in one dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. Our main result shows the existence, uniqueness (up to…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
This paper focuses on traveling wave solutions for the so-called Rosenzweig-MacArthur model with spatial diffusion. The main results of this note are concerned with the existence and uniqueness of traveling wave solution as well as periodic…
The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it…
We consider reaction-diffusion equations of porous medium type, with different kind of reaction terms, and nonnegative bounded initial data. For all the reaction terms under consideration there are initial data for which the solution…
We study travelling-wave solutions for a reaction-diffusion system arising as a model for host-tissue degradation by bacteria. This system consists of a parabolic equation coupled with an ordinary differential equation. For large values of…
Stability of the kink-like and soliton-like travelling wave solutions to the generalized convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
We investigate the connection between the existence of an explicit travelling wave solution and the travelling wave with minimal speed in a scalar monostable reaction-diffusion equation.
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with…
We study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1-D Euclidean space. The diffusion coefficient depends on the gradient in analogy with the p-Laplacian and may be degenerate.…
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…
We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower…
We use a simple method that leads to the integrals involved in obtaining the traveling wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in…
In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very broad framework using simple real analysis tools. In…
In this paper the travelling wave solutions in the adiabatic model with two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The…
In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction-diffusion equations, and we will apply our…