On the equivalence of viscosity solutions and distributional solutions for the time-fractional diffusion equation

被引：9

作者：

Giga, Yoshikazu ^{[1
]}

Mitake, Hiroyoshi ^{[1
]}

Sato, Shoichi ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 1538914, Japan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 316卷

关键词：

Caputo time fractional derivatives; Initial-boundary value problems; Fractional diffusion equation; Viscosity solutions; Distributional solutions; HAMILTON-JACOBI EQUATIONS; WEAK SOLUTIONS;

D O I：

10.1016/j.jde.2022.01.057

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider an initial-boundary value problem for the time-fractional diffusion equation. We prove the equivalence of two notions of weak solutions, viscosity solutions and distributional solutions. (c) 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页码：364 / 386

页数：23

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