Nonlinear evolution equations that are non-local in space and time
We deal with a nonlocal nonlinear evolution problem of the form ∬Rn×RJ(x−y,t−s)|v‾(y,s)−v(x,t)|p−2(v‾(y,s)−v(x,t))dyds=0 for (x,t)∈Rn×[0,∞). Here p≥2, J:Rn+1→R is a nonnegative kernel, compactly supported inside the set {(x,t)∈Rn+1:t≥0} with ∬Rn×RJ(x,t)dxdt=1 and v‾ stands for an extension of a give...
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todo:paper_0022247X_v455_n2_p1470_Beltritti2023-10-03T14:29:23Z Nonlinear evolution equations that are non-local in space and time Beltritti, G. Rossi, J.D. Mean value properties Nonlocal evolution problems p-Laplacian We deal with a nonlocal nonlinear evolution problem of the form ∬Rn×RJ(x−y,t−s)|v‾(y,s)−v(x,t)|p−2(v‾(y,s)−v(x,t))dyds=0 for (x,t)∈Rn×[0,∞). Here p≥2, J:Rn+1→R is a nonnegative kernel, compactly supported inside the set {(x,t)∈Rn+1:t≥0} with ∬Rn×RJ(x,t)dxdt=1 and v‾ stands for an extension of a given initial value f, that is, v‾(x,t)={v(x,t)t≥0,f(x,t)t<0. For this problem we prove existence and uniqueness of a solution. In addition, we show that the solutions approximate viscosity solutions to the local nonlinear PDE ‖∇u‖p−2ut=Δpu when the kernel is rescaled in a suitable way. © 2017 Elsevier Inc. 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_0022247X_v455_n2_p1470_Beltritti |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Mean value properties Nonlocal evolution problems p-Laplacian |
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Mean value properties Nonlocal evolution problems p-Laplacian Beltritti, G. Rossi, J.D. Nonlinear evolution equations that are non-local in space and time |
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Mean value properties Nonlocal evolution problems p-Laplacian |
| description |
We deal with a nonlocal nonlinear evolution problem of the form ∬Rn×RJ(x−y,t−s)|v‾(y,s)−v(x,t)|p−2(v‾(y,s)−v(x,t))dyds=0 for (x,t)∈Rn×[0,∞). Here p≥2, J:Rn+1→R is a nonnegative kernel, compactly supported inside the set {(x,t)∈Rn+1:t≥0} with ∬Rn×RJ(x,t)dxdt=1 and v‾ stands for an extension of a given initial value f, that is, v‾(x,t)={v(x,t)t≥0,f(x,t)t<0. For this problem we prove existence and uniqueness of a solution. In addition, we show that the solutions approximate viscosity solutions to the local nonlinear PDE ‖∇u‖p−2ut=Δpu when the kernel is rescaled in a suitable way. © 2017 Elsevier Inc. |
| format |
JOUR |
| author |
Beltritti, G. Rossi, J.D. |
| author_facet |
Beltritti, G. Rossi, J.D. |
| author_sort |
Beltritti, G. |
| title |
Nonlinear evolution equations that are non-local in space and time |
| title_short |
Nonlinear evolution equations that are non-local in space and time |
| title_full |
Nonlinear evolution equations that are non-local in space and time |
| title_fullStr |
Nonlinear evolution equations that are non-local in space and time |
| title_full_unstemmed |
Nonlinear evolution equations that are non-local in space and time |
| title_sort |
nonlinear evolution equations that are non-local in space and time |
| url |
http://hdl.handle.net/20.500.12110/paper_0022247X_v455_n2_p1470_Beltritti |
| work_keys_str_mv |
AT beltrittig nonlinearevolutionequationsthatarenonlocalinspaceandtime AT rossijd nonlinearevolutionequationsthatarenonlocalinspaceandtime |
| _version_ |
1807323284145963008 |