Global convergence in a reaction-diffusion equation with piecewise constant argument

✍ Scribed by H.M. Byrne; S.A. Gourley

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 346 KB
• Volume: 34
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(01)00071-1

✦ Synopsis

In this paper, we consider the reaction-diffusion equation with piecewise constant argument

on a finite domain, with r, E, D > 0. By employing the method of sub-and super-solutions we prove that, under the condition E < r(1 -exp(-r)), all solutions with positive initial data converge to the positive uniform state.