A nonlocal convection-diffusion equation
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 cond...
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todo:paper_00221236_v251_n2_p399_Ignat2023-10-03T14:27:14Z A nonlocal convection-diffusion equation Ignat, L.I. Rossi, J.D. Asymptotic behaviour Convection-diffusion Nonlocal diffusion 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00221236_v251_n2_p399_Ignat |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Asymptotic behaviour Convection-diffusion Nonlocal diffusion |
| spellingShingle |
Asymptotic behaviour Convection-diffusion Nonlocal diffusion Ignat, L.I. Rossi, J.D. A nonlocal convection-diffusion equation |
| topic_facet |
Asymptotic behaviour Convection-diffusion Nonlocal diffusion |
| description |
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. |
| format |
JOUR |
| author |
Ignat, L.I. Rossi, J.D. |
| author_facet |
Ignat, L.I. Rossi, J.D. |
| author_sort |
Ignat, L.I. |
| title |
A nonlocal convection-diffusion equation |
| title_short |
A nonlocal convection-diffusion equation |
| title_full |
A nonlocal convection-diffusion equation |
| title_fullStr |
A nonlocal convection-diffusion equation |
| title_full_unstemmed |
A nonlocal convection-diffusion equation |
| title_sort |
nonlocal convection-diffusion equation |
| url |
http://hdl.handle.net/20.500.12110/paper_00221236_v251_n2_p399_Ignat |
| work_keys_str_mv |
AT ignatli anonlocalconvectiondiffusionequation AT rossijd anonlocalconvectiondiffusionequation AT ignatli nonlocalconvectiondiffusionequation AT rossijd nonlocalconvectiondiffusionequation |
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1807319084153438208 |