Entire solutions in reaction-advection-diffusion equations in cylinders

Entire Solutions of Reaction-diffusion Equations with Balanced Bistable Nonlinearities

This paper deals with entire solutions of a bistable reaction-diffusion equation for which the speed of the traveling wave connecting two constant stable equilibria is zero. Entire solutions which behave as two traveling fronts approaching, with super-slow speeds, from opposite directions and annihilating in a finite time are constructed by using a quasiinvariant manifold approach. Such solutio...

Numerical Solution of Advection-Diffusion-Reaction Equations

Multiplicity of supercritical fronts for reaction-diffusion equations in cylinders

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 connecting an unstable equilibrium to the closest stable equilibrium for all speeds exceeding a critical value. We show that these are, in fact, the only trav...

Entire Solutions in Bistable Reaction-diffusion Equations with Nonlocal Delayed Nonlinearity

This paper is concerned with entire solutions for bistable reactiondiffusion equations with nonlocal delay in one-dimensional spatial domain. Here the entire solutions are defined in the whole space and for all time t ∈ R. Assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument, we prove the existence of entire solutions whi...

A Framework for Exploring Numerical Solutions of Advection- Reaction-Diffusion Equations Using a GPU-Based Approach

In this paper we describe a general purpose, graphics processing unit (GP-GPU)-based approach for solving partial differential equations (PDEs) within advection-reactiondiffusion models. The GP-GPU-based approach provides a platform for solving PDEs in parallel and can thus significantly reduce solution times over traditional CPU implementations. This allows for a more efficient exploration of ...