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Abstract:

We study the behavior of the heat content for a nonlocal evolution problem. We obtain an asymptotic expansion for the heat content of a set D, defined as HDJ(t) := ∫D u(x,t)dx, with u being the solution to ut = J∗u-u with initial condition u0 = χD. This expansion is given in terms of geometric values of D. As a consequence, we obtain that HD(t)=|D|-PJ(D)t + o(t) as t↓ 0. We also recover the usual heat content for the heat equation when we rescale the kernel J in an appropriate way. Finally, we also find an asymptotic expansion for the nonlocal analogous to the spectral heat content that is defined as before but considering u(x,t) a solution to the equation ut = J∗u-u inside D with u = 0 in RN|D and initial condition u0 = χD. © 2017 by De Gruyter.

Registro:

Documento: Artículo
Título:The Heat Content for Nonlocal Diffusion with Non-singular Kernels
Autor:Mazón, J.M.; Rossi, J.D.; Toledo, J.
Filiación:Departament d'Anàlisi Matemàtica, Universitat de València, Dr. Moliner 50, Burjassot, 46100, Spain
Departamento de Matemáticas, FCEyN, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Palabras clave:Heat Content; Non-Singular Kernels; Nonlocal Evolution Problems
Año:2017
Volumen:17
Número:2
Página de inicio:255
Página de fin:268
DOI: http://dx.doi.org/10.1515/ans-2017-0005
Título revista:Advanced Nonlinear Studies
Título revista abreviado:Adv. Nonlinear Stud.
ISSN:15361365
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_15361365_v17_n2_p255_Mazon

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Citas:

---------- APA ----------
Mazón, J.M., Rossi, J.D. & Toledo, J. (2017) . The Heat Content for Nonlocal Diffusion with Non-singular Kernels. Advanced Nonlinear Studies, 17(2), 255-268.
http://dx.doi.org/10.1515/ans-2017-0005
---------- CHICAGO ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "The Heat Content for Nonlocal Diffusion with Non-singular Kernels" . Advanced Nonlinear Studies 17, no. 2 (2017) : 255-268.
http://dx.doi.org/10.1515/ans-2017-0005
---------- MLA ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "The Heat Content for Nonlocal Diffusion with Non-singular Kernels" . Advanced Nonlinear Studies, vol. 17, no. 2, 2017, pp. 255-268.
http://dx.doi.org/10.1515/ans-2017-0005
---------- VANCOUVER ----------
Mazón, J.M., Rossi, J.D., Toledo, J. The Heat Content for Nonlocal Diffusion with Non-singular Kernels. Adv. Nonlinear Stud. 2017;17(2):255-268.
http://dx.doi.org/10.1515/ans-2017-0005