Linear subdiffusion in weighted fractional Hölder spaces

Mykola Krasnoschok; Nataliya Vasylyeva

doi:10.3934/eect.2021050

Article Contents

2022, Volume 11, Issue 4: 1455-1487. Doi: 10.3934/eect.2021050

This issue Previous Article Sufficient conditions for the continuity of inertial manifolds for singularly perturbed problems Next Article

Linear subdiffusion in weighted fractional Hölder spaces

Mykola Krasnoschok¹ and
Nataliya Vasylyeva^2,

1.
Institute of Applied Mathematics and Mechanics of NAS of Ukraine, G.Batyuka str. 19, 84100 Sloviansk, Ukraine
2.
Institute of Applied Mathematics and Mechanics of NAS of Ukraine, G.Batyuka str. 19, 84100 Sloviansk, Ukraine and, Institute of Hydromechanics of NAS of Ukraine, Zhelyabova str. 8/4, 03057 Kyiv, Ukraine

^* Corresponding author: N. Vasylyeva
^* Corresponding author: N. Vasylyeva

Received: December 31, 2020

Revised: April 30, 2021

Early access: September 2021

Published: August 2022

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Abstract

For $ \nu\in(0,1) $, we investigate the nonautonomous subdiffusion equation:

$ \mathbf{D}_{t}^{\nu}u-\mathcal{L}u = f(x,t), $

where $ \mathbf{D}_{t}^{\nu} $ is the Caputo fractional derivative and $ \mathcal{L} $ is a uniformly elliptic operator with smooth coefficients depending on time. Under suitable conditions on the given data and a minimal number (i.e. the necessary number) of compatibility conditions, the global classical solvability to the related initial-boundary value problems are established in the weighted fractional Hölder spaces.

Keywords:

Mathematics Subject Classification: Primary: 35R11, 35C15; Secondary: 35B45, 26A33.

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