School of Mathematical & Statistical Sciences Faculty Publications and Presentations

Traveling wavefronts for density-dependent diffusion reaction convection equation with time delay

Document Type

Article

Publication Date

3-30-2024

Abstract

We are concerned with the existence of traveling waves for density-dependent diffusion reaction nonlinear convection equations with small time delay. We first study the existence and uniqueness of smooth and sharp-type traveling wavefront solution of the wave speed c ≥ c∗ for equation without time delay, where c∗ is the minimal wave speed. Meanwhile, we construct a variational principle for c∗ from which the upper bound of c∗ is determined, while the lower bound of c∗ is attained by using the phase plane analysis. Then, we obtain the existence of smooth traveling wavefront solution for equation with small time delay for c > c∗ by applying the perturbation method and implicit function theorem.

Comments

© 2021 John Wiley & Sons, Ltd.

Publication Title

Mathematical Methods in the Applied Sciences

DOI

10.1002/mma.7288

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