Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data
We study the large time behavior of nonnegative solutions of the Cauchy problem ut =R J(x,y)(u(y; t),u(x; t)) dy,up, u(x; 0) = u0(x) 2 L∞, where |x|αu0(x) → A < 0 as |x| → 1. One of our main goals is the study of the critical case p = 1+2=ff for 0 > ff > N, left open in previous articles, f...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10780947_v31_n2_p581_Terra |
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paperaa:paper_10780947_v31_n2_p581_Terra2023-06-12T16:49:36Z Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data Discrete Contin. Dyn. Syst. 2011;31(2):581-605 Terra, J. Wolanski, N. Large time behavior Nonlocal diffusion We study the large time behavior of nonnegative solutions of the Cauchy problem ut =R J(x,y)(u(y; t),u(x; t)) dy,up, u(x; 0) = u0(x) 2 L∞, where |x|αu0(x) → A < 0 as |x| → 1. One of our main goals is the study of the critical case p = 1+2=ff for 0 > ff > N, left open in previous articles, for which we prove that tff=2ju(x; t) , U(x; t)j → 0 where U is the solution of the heat equation with absorption with initial datum U(x; 0) = CA;N |x|,α. Our proof, involving sequences of rescalings of the solution, allows us to establish also the large time behavior of solutions having more general nonintegrable initial data u0 in the supercritical case and also in the critical case (p = 1 + 2=N) for bounded and integrable u0. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2011 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10780947_v31_n2_p581_Terra |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
Large time behavior Nonlocal diffusion |
| spellingShingle |
Large time behavior Nonlocal diffusion Terra, J. Wolanski, N. Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
| topic_facet |
Large time behavior Nonlocal diffusion |
| description |
We study the large time behavior of nonnegative solutions of the Cauchy problem ut =R J(x,y)(u(y; t),u(x; t)) dy,up, u(x; 0) = u0(x) 2 L∞, where |x|αu0(x) → A < 0 as |x| → 1. One of our main goals is the study of the critical case p = 1+2=ff for 0 > ff > N, left open in previous articles, for which we prove that tff=2ju(x; t) , U(x; t)j → 0 where U is the solution of the heat equation with absorption with initial datum U(x; 0) = CA;N |x|,α. Our proof, involving sequences of rescalings of the solution, allows us to establish also the large time behavior of solutions having more general nonintegrable initial data u0 in the supercritical case and also in the critical case (p = 1 + 2=N) for bounded and integrable u0. |
| format |
Artículo Artículo publishedVersion |
| author |
Terra, J. Wolanski, N. |
| author_facet |
Terra, J. Wolanski, N. |
| author_sort |
Terra, J. |
| title |
Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
| title_short |
Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
| title_full |
Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
| title_fullStr |
Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
| title_full_unstemmed |
Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
| title_sort |
large time behavior for a nonlocal diffusion equation with absorption and bounded initial data |
| publishDate |
2011 |
| url |
http://hdl.handle.net/20.500.12110/paper_10780947_v31_n2_p581_Terra |
| work_keys_str_mv |
AT terraj largetimebehaviorforanonlocaldiffusionequationwithabsorptionandboundedinitialdata AT wolanskin largetimebehaviorforanonlocaldiffusionequationwithabsorptionandboundedinitialdata |
| _version_ |
1769810191626272768 |