STABILITY OF TIME-PERIODIC TRAVELING FRONTS IN BISTABLE REACTION-ADVECTION-DIFFUSION EQUATIONS

This paper is concerned with the global exponential stability of time periodic traveling fronts of reaction-advection-diffusion equations with time periodic bistable nonlinearity in infinite cylinders. It is well known that such traveling fronts exist and are asymptotically stable. In this paper, we further show that such fronts are globally exponentially stable. The main difficulty is to construct appropriate supersolutions and subsolutions.

Entire solutions in reaction-advection-diffusion equations with bistable nonlinearities in heterogeneous media

This paper is concerned with entire solutions ( t ∈ R) for bistable reaction-advection-diffusion equations in heterogeneous media. By using traveling curved fronts connecting a constant unstable stationary state and a stable stationary state, we proved that there exist entire solutions behaving as two traveling curved fronts coming from opposite directions, and approaching each other. Furthermore, we prove that such an entire solution is unique and Liapunov stable. The key technique is to characterize the asymptotic behavior of solutions at infinity in term of appropriate subsolutions and supersolutions.

Wave solutions and numerical validation for the coupled reaction-advection-diffusion dynamical model in a porous medium

The current study examines the special class of a generalized reaction-advection-diffusion dynamical model that is called the system of coupled Burger’s equations.This system plays a vital role in the essential areas of physics,including fluid dynamics and acoustics.Moreover,two promising analytical integration schemes are employed for the study;in addition to the deployment of an efficient variant of the eminent Adomian decomposition method.Three sets of analytical wave solutions are revealed,including exponential,periodic,and dark-singular wave solutions;while an amazed rapidly convergent approximate solution is acquired on the other hand.At the end,certain graphical illustrations and tables are provided to support the reported analytical and numerical results.No doubt,the present study is set to bridge the existing gap between the analytical and numerical approaches with regard to the solution validity of various models of mathematical physics.

Sufficient noise and turbulence can induce phytoplankton patchiness

Phytoplankton patchiness ubiquitously obser- ved in marine ecosystems is a simple phy- sical phenomenon. Only two factors are required for its formation: one is persistent variations of inhomogeneous distributions in the phytopl- ankton population and the other is turbulent stirring by eddies. It is not necessary to assume continuous oscillations such as limit cycles for realization of the first factor. Instead, a certain amount of noise is enough. Random fluctua-tions by environmental noise and turbulent ad-vection by eddies seem to be common in open oceans. Based on these hypotheses, we pro-pose seemingly the simplest method to simulate patchiness formation that can create realistic images. Sufficient noise and turbulence can induce patchiness formation even though the system lies on the stable equilibrium conditions. We tentatively adopt the two-component model with nutrients and phytoplankton, however, the choice of the mathematical model is not essen-tial. The simulation method proposed in this study can be applied to whatever model with stable equilibrium states including one-com-ponent ones.

Blowup of the Solutions for a Reaction-Advection- Diffusion Equation with Free Boundaries

We investigate a blowup problem of a reaction-advection-diffusion equa-tion with double free boundaries and aim to use the dynamics of such a problem to describe the heat transfer and temperature change of a chemical reaction in advective environment with the free boundary representing the spreading front of the heat.We study the influence of the advection on the blowup properties of the solutions and con-clude that large advection is not favorable for blowup.Moreover,we give the decay estimates of solutions and the two free boundaries converge to a finite limit for small initial data.