Related papers: Traveling waves for a boundary reaction-diffusion …
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels,…
We investigate traveling wave solutions for a nonlinear system of two coupled reaction-diffusion equations characterized by double degenerate diffusivity: \[n_t= -f(n,b), \quad b_t=[g(n)h(b)b_x]_x+f(n,b).\] These systems mainly appear in…
In this paper we study the isolated periodic traveling wave solutions of a family of reaction-convection-diffusion equations with cubic reaction term. Existence/nonexistence of periodic traveling wave solutions are discussed in different…
In this paper, the existence of a non-trivial, positive and bounded critical traveling wave solution of a diffusive disease model, whose reaction system has infinity many equilibria, is obtained for the first time. This gives an affirmative…
We consider the propagation of a flame front in a solid periodic medium. The model is governed by a free boundary system in which the front's velocity depends on the temperature via a kinetic rate which may degenerate. We show the existence…
We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess traveling wave solutions…
The paper is devoted to a reaction-diffusion equation with delay arising in modelling the immune response. We prove the existence of travelling waves in the bistable case using the Leray-Schauder method. In difference with the previous…
We investigate a model of solid propellant combustion involving surface pyrolysis coupled to finite activation energy gas phase combustion. Existence and uniqueness of a travelling wave solution are established by extending dynamical system…
We analyze travelling wave (TW) solutions for nonlinear systems consisting of an ODE coupled to a degenerate PDE with a diffusion coefficient that vanishes as the solution tends to zero and blows up as it approaches its maximum value.…
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…
Lubrication equations for a surfactant-driven flow of a thin layer of fluid are considered with a singular surfactant-dependent surface tension. It is shown that there exists a bounded traveling wave solution which connects a fully…
We prove the existence of a family of travelling wave solutions in a variant of the $\textit{Zeldovich-Frank-Kamenetskii (ZFK) equation}$, a reaction-diffusion equation which models the propagation of planar laminar premixed flames in…
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…
The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous…
The Fisher-KPP equation with general nonlinear diffusion and arbitrary kinetic orders in the reaction terms is considered. The existence of oscillatory travelling wave solutions is proved for this model. Conditions for the existence of such…
In this paper we prove the existence of finite traveling-wave type solutions to the nonlinear double degenerate parabolic equation of turbulent filtration with absorption.
We investigate in this paper a scalar reaction diffusion equation with a nonlinear reaction term depending on x-ct. Here, c is a prescribed parameter modelling the speed of climate change and we wonder whether a population will survive or…
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…
We give sufficient conditions for the existence of positive travelling wave solutions for multi-dimensional autonomous reaction-diffusion systems with distributed delay. To prove the existence of travelling waves, we give an abstract…
We study the boundary value problem for nonlinear fourth-order partial differential equation with jumping nonlinearity which can serve, e.g., as a model of an asymmetrically supported bending beam. We focus on a special type of solutions,…