We consider a coupled reaction–advection–diffusion system based on the Fisher-KPP and Burgers equations. These equations serve as one-dimensional version of model for reacting fluid in which arising density differences induce buoyancy force advecting fluid. study front propagation this through lens traveling waves solutions. are able to show two quite different behaviors depending whether coupl...

The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves of finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves tends to infinity, their velocities ap...

case II diffusion of a penetrant through a polymer matrix is characterized by constant front speed. Hence, a traveling-wave analysis is appropriate for the model equations. For the previously validated model analyzed here, conditions on the molecular and stress diffusion coefficients are obtained which guarantee the existence of a traveling wave. Conditions are derived under which an interior m...

We formulate an integro-difference model to predict the growth and spatial spread of a plant population with an age-structured seed bank and juvenile cohort. We allow the seeds in the bank to be of any age, producing a system of infinitely many equations. We assume that juvenile plants mature into adults at a particular age. The production of new seeds can be densitydependent and so the functio...

Based on Codeço's cholera model (2001), an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speed c (∗) is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder's fixed point theorem is applied. The nonexistence of traveling wave solu...