A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions
In this paper we discuss a nonlocal approximation to the classical heat equation with Neumann boundary conditions. We consider. wt(small element of)(x,t)=1(small element of)N+2∫ΩJx-y(small element of)(w(small element of)(y,t)-w(small element of)(x,t))dy+C1(small element of)N∫∂ΩJx-y(small element of)...
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| Formato: | INPR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10183647_v_n_p_Gomez |
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todo:paper_10183647_v_n_p_Gomez2023-10-03T15:56:29Z A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions Gómez, C.A. Rossi, J.D. 35K05 45A05 45J05 Heat equation Neumann boundary conditions Nonlocal diffusion In this paper we discuss a nonlocal approximation to the classical heat equation with Neumann boundary conditions. We consider. wt(small element of)(x,t)=1(small element of)N+2∫ΩJx-y(small element of)(w(small element of)(y,t)-w(small element of)(x,t))dy+C1(small element of)N∫∂ΩJx-y(small element of)g(y,t)dSy,(x,t)∈Ω[U+203E]×(0,T),w(x,0)=u0(x),x∈Ω[U+203E],and we show that the corresponding solutions, w(small element of), converge to the classical solution of the local heat equation vt=δv with Neumann boundary conditions, ∂v∂n(x,t)=g(x,t), and initial condition v(0)=u0, as the parameter (small element of) goes to zero. The obtained convergence is in the weak star on L∞ topology. © 2017 The Authors. INPR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10183647_v_n_p_Gomez |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
35K05 45A05 45J05 Heat equation Neumann boundary conditions Nonlocal diffusion |
| spellingShingle |
35K05 45A05 45J05 Heat equation Neumann boundary conditions Nonlocal diffusion Gómez, C.A. Rossi, J.D. A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions |
| topic_facet |
35K05 45A05 45J05 Heat equation Neumann boundary conditions Nonlocal diffusion |
| description |
In this paper we discuss a nonlocal approximation to the classical heat equation with Neumann boundary conditions. We consider. wt(small element of)(x,t)=1(small element of)N+2∫ΩJx-y(small element of)(w(small element of)(y,t)-w(small element of)(x,t))dy+C1(small element of)N∫∂ΩJx-y(small element of)g(y,t)dSy,(x,t)∈Ω[U+203E]×(0,T),w(x,0)=u0(x),x∈Ω[U+203E],and we show that the corresponding solutions, w(small element of), converge to the classical solution of the local heat equation vt=δv with Neumann boundary conditions, ∂v∂n(x,t)=g(x,t), and initial condition v(0)=u0, as the parameter (small element of) goes to zero. The obtained convergence is in the weak star on L∞ topology. © 2017 The Authors. |
| format |
INPR |
| author |
Gómez, C.A. Rossi, J.D. |
| author_facet |
Gómez, C.A. Rossi, J.D. |
| author_sort |
Gómez, C.A. |
| title |
A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions |
| title_short |
A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions |
| title_full |
A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions |
| title_fullStr |
A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions |
| title_full_unstemmed |
A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions |
| title_sort |
nonlocal diffusion problem that approximates the heat equation with neumann boundary conditions |
| url |
http://hdl.handle.net/20.500.12110/paper_10183647_v_n_p_Gomez |
| work_keys_str_mv |
AT gomezca anonlocaldiffusionproblemthatapproximatestheheatequationwithneumannboundaryconditions AT rossijd anonlocaldiffusionproblemthatapproximatestheheatequationwithneumannboundaryconditions AT gomezca nonlocaldiffusionproblemthatapproximatestheheatequationwithneumannboundaryconditions AT rossijd nonlocaldiffusionproblemthatapproximatestheheatequationwithneumannboundaryconditions |
| _version_ |
1807318408368226304 |