A nonlocal convection-diffusion equation

• Autores: Ignat, L.I.; Rossi, J.D.
• Año de publicación: 2007
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: J. Funct. Anal. 2007;251(2):399-437
• Materia: Asymptotic behaviour; Convection-diffusion; Nonlocal diffusion
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut = J * u - u + G * (f (u)) - f (u) in Rd, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection-diffusion equation ut = Δ u + b ṡ ∇ (f (u)). In fact, we prove that solutions of the nonlocal equation converge to the solution of the usual convection-diffusion equation when we rescale the convolution kernels J and G appropriately. Finally we study the asymptotic behaviour of solutions as t → ∞ when f (u) = | u |q - 1 u with q > 1. We find the decay rate and the first-order term in the asymptotic regime. © 2007 Elsevier Inc. All rights reserved.
Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.