The large time behavior of solutions of a diffusion equation involving a nonlocal convection term

Abstract

We study the existence, uniqueness, and asymtotic behaviour of non-negative solutions to a parabolic diffusion equation involving a nonlocal con-vective term on a bounded domain ? contained in Rⁿ. We apply the In variance Principle of LaSalle and Hale to prove that the solution tends to zero as t → ∞

Keywords:

• Parabolic PDEs
• large time behavior
• nonlocal convective terms

^∗Current address: Department of Mathematics, U.S. Naval Academy, Annapolis, Maryland 21402

^∗Current address: Department of Mathematics, U.S. Naval Academy, Annapolis, Maryland 21402

Notes

^∗Current address: Department of Mathematics, U.S. Naval Academy, Annapolis, Maryland 21402