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Abstract:

Let J: ℝ → ℝ be a nonnegative, smooth function with ∫ℝ J(r)dr = 1, supported in [-1, 1], symmetric, J(r) = J(-r), and strictly increasing in [-1,0]. We consider the Neumann boundary value problem for a nonlocal, nonlinear operator that is similar to the porous medium, and we study the equation ut(x, t)=∫L-L(J(x-y/ u(y,t) - J(x-y/u(x, t))dy, x∈[-L, L].We prove existence and uniqueness of solutions and a comparison principle. We find the asymptotic behaviour of the solutions as t → ∞: they converge to the mean value of the initial data. Next, we consider a discrete version of the above problem. Under suitable hypotheses we prove that the discrete model has properties analogous to the continuous one. Moreover, solutions of the discrete problem converge to the continuous ones when the mesh parameter goes to zero. Finally, we perform some numerical experiments. © 2007 American Mathematical Society.

Registro:

Documento: Artículo
Título:Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models
Autor:Bogoya, M.; Ferreira, R.; Rossi, J.D.
Filiación:Depto. de Matemática, Univ. Católica de Chile, Santiago, Chile
Depto. de Matemática, Univ. Nacional de Colombia, Bogotá, Colombia
Depto. de Matemática, U. Carlos III, 28911, Leganés, Spain
IMAFF, CSIC, Serrano 117, Madrid, Spain
Depto. Matematica, FCEyN, UBA, Buenos Aires, Argentina
Palabras clave:Neumann boundary conditions; Nonlocal diffusion
Año:2007
Volumen:135
Número:12
Página de inicio:3837
Página de fin:3846
DOI: http://dx.doi.org/10.1090/S0002-9939-07-09205-2
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00029939_v135_n12_p3837_Bogoya.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v135_n12_p3837_Bogoya

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Citas:

---------- APA ----------
Bogoya, M., Ferreira, R. & Rossi, J.D. (2007) . Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models. Proceedings of the American Mathematical Society, 135(12), 3837-3846.
http://dx.doi.org/10.1090/S0002-9939-07-09205-2
---------- CHICAGO ----------
Bogoya, M., Ferreira, R., Rossi, J.D. "Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models" . Proceedings of the American Mathematical Society 135, no. 12 (2007) : 3837-3846.
http://dx.doi.org/10.1090/S0002-9939-07-09205-2
---------- MLA ----------
Bogoya, M., Ferreira, R., Rossi, J.D. "Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models" . Proceedings of the American Mathematical Society, vol. 135, no. 12, 2007, pp. 3837-3846.
http://dx.doi.org/10.1090/S0002-9939-07-09205-2
---------- VANCOUVER ----------
Bogoya, M., Ferreira, R., Rossi, J.D. Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models. Proc. Am. Math. Soc. 2007;135(12):3837-3846.
http://dx.doi.org/10.1090/S0002-9939-07-09205-2