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Abstract:

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.

Registro:

Documento: Artículo
Título:Nonlinear evolution equations that are non-local in space and time
Autor:Beltritti, G.; Rossi, J.D.
Filiación:CONICET, Departamento de Matemática, FCEFQyN, Universidad Nacional de Río Cuarto, Ruta Nac. 36 Km 601, Río Cuarto, Córdoba 5800, Argentina
CONICET, Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellon I, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Palabras clave:Mean value properties; Nonlocal evolution problems; p-Laplacian
Año:2017
Volumen:455
Número:2
Página de inicio:1470
Página de fin:1504
DOI: http://dx.doi.org/10.1016/j.jmaa.2017.06.059
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v455_n2_p1470_Beltritti

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Citas:

---------- APA ----------
Beltritti, G. & Rossi, J.D. (2017) . Nonlinear evolution equations that are non-local in space and time. Journal of Mathematical Analysis and Applications, 455(2), 1470-1504.
http://dx.doi.org/10.1016/j.jmaa.2017.06.059
---------- CHICAGO ----------
Beltritti, G., Rossi, J.D. "Nonlinear evolution equations that are non-local in space and time" . Journal of Mathematical Analysis and Applications 455, no. 2 (2017) : 1470-1504.
http://dx.doi.org/10.1016/j.jmaa.2017.06.059
---------- MLA ----------
Beltritti, G., Rossi, J.D. "Nonlinear evolution equations that are non-local in space and time" . Journal of Mathematical Analysis and Applications, vol. 455, no. 2, 2017, pp. 1470-1504.
http://dx.doi.org/10.1016/j.jmaa.2017.06.059
---------- VANCOUVER ----------
Beltritti, G., Rossi, J.D. Nonlinear evolution equations that are non-local in space and time. J. Math. Anal. Appl. 2017;455(2):1470-1504.
http://dx.doi.org/10.1016/j.jmaa.2017.06.059