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

DOI10.1016/j.jde.2022.01.057zbMath1484.35378arXiv2108.11065OpenAlexW3193495096MaRDI QIDQ2669925

Shoichi Sato, Yoshikazu Giga, Hiroyoshi Mitake

Publication date: 9 March 2022

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.11065

zbMATH Keywords

initial-boundary value problemsviscosity solutionsdistributional solutionsfractional diffusion equationCaputo time fractional derivatives

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Weak solutions to PDEs (35D30) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Viscosity solutions to PDEs (35D40) Fractional partial differential equations (35R11)

Related Items (5)

A class of nonlocal impulsive differential equations with conformable fractional derivative ⋮ On the blow-up of solutions for a fractional diffusion equation with nonlinear memory and reaction terms in a bounded domain ⋮ On the rate of convergence in homogenization of time-fractional Hamilton-Jacobi equations ⋮ The Cauchy problem for time-fractional linear nonlocal diffusion equations ⋮ Monotone iterations method for fractional diffusion equations

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