Approximate wave fronts in a class of reaction-diffusion equations
نویسنده
چکیده
Under special conditions an approximate wave front solution to a system of nonlinear reaction-diffusion type equations is obtained. An assumption of fast kinetics permits the system to be reformulated as a single nonlinear differential-integral equation of convolution type. If the convolution kernel has the form of a mollifier then the convolution is localized to obtain an infinite system of differential equations. In some cases the system can be truncated and solved to obtain approximate wave fronts. Examples of this method are presented, one with nonlinear convection and one with nonlinear diffusion.
منابع مشابه
Dynamical Behaviors of a Delayed Reaction-diffusion Equation
In this paper, we derive a delayed reaction-diffusion equation to describe a two-species predator-prey system with diffusion terms and stage structure. By coupling the uniformly approximate approach with the method of upper and lower solutions, we prove that the traveling wave fronts exist, which connect the zero solution with the positive steady state. Finally, we draw a conclusion that the ex...
متن کاملUniqueness of monostable pulsating wave fronts for time periodic reaction-diffusion equations
Keywords: Reaction–diffusion equations Pulsating wave fronts KPP and monostable nonlinearities Uniqueness a b s t r a c t We establish the uniqueness of pulsating wave fronts for reaction–diffusion equations in time periodic media with monostable nonlinearities. For the Kolmogorov–Petrovsky– Piskunov (KPP) type nonlinearity, this result provides a complete classification of all types of KPP pul...
متن کاملUniqueness of Monotone Mono-stable Waves for Reaction-Diffusion Equations with Time Delay
Many models in biology and ecology can be described by reaction-diffusion equations wit time delay. One of important solutions for these type of equations is the traveling wave solution that shows the phenomenon of wave propagation. The existence of traveling wave fronts has been proved for large class of equations, in particular, the monotone systems, such as the cooperative systems and some c...
متن کاملA numerical investigation of a reaction-diffusion equation arises from an ecological phenomenon
This paper deals with the numerical solution of a class of reaction diffusion equations arises from ecological phenomena. When two species are introduced into unoccupied habitat, they can spread across the environment as two travelling waves with the wave of the faster reproducer moving ahead of the slower.The mathematical modelling of invasions of species in more complex settings that include ...
متن کاملa New Approximate Solution Technique (Quantized Method) for Simultaneous Gas Solid Reactions
Simultaneous reactions between solids and gases are very important in the chemical and metallurgical processes. In the modeling, the chemical reaction and diffusion of gases must be considered. Therefore, a set of coupled partial differential equations is found. When the kinetic is a function of solid concentration, there is not any analytical solution for these equations. Therefore, numerical ...
متن کامل