Existence and uniqueness for parabolic problems with Caputo time derivative

被引：35

作者：

Topp, Erwin ^{[1
]}

Yangari, Miguel ^{[2
,3
]}

机构：

[1] Univ Santiago de Chile, Dept Matemat & CC, Casilla 307, Santiago, Chile

[2] Escuela Politec Nacl, Res Ctr Math Modelling MODEMAT, Ladron de Guevara E11-253,POB 17-01-2759, Quito, Ecuador

[3] Escuela Politec Nacl, Dept Matemat, Ladron de Guevara E11-253,POB 17-01-2759, Quito, Ecuador

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 262卷 / 12期

关键词：

Viscosity solutions; Caputo derivative; Nonlocal operator; Comparison principle; Large time behavior; FRACTIONAL CAUCHY-PROBLEMS; HAMILTON-JACOBI EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS; VISCOSITY SOLUTIONS; RANDOM-WALKS; DIFFUSION; GUIDE;

D O I：

10.1016/j.jde.2017.02.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we are interested in the well-posedness of fully nonlinear Cauchy problems in which the time derivative is of Caputo type. We address this question in the framework of viscosity solutions, obtaining the existence via Perron's method, and comparison for bounded sub and supersolutions by a suitable regularization through inf and sup convolution in time. As an application, we prove the steady-state large time behavior in the case of proper nonlinearities and provide a rate of convergence by using the Mittag Leffler operator. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：6018 / 6046

页数：29

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