Open Access
2018 Solvability of linear boundary value problems for subdiffusion equations with memory
Mykola Krasnoschok, Vittorino Pata, Nataliya Vasylyeva
J. Integral Equations Applications 30(3): 417-445 (2018). DOI: 10.1216/JIE-2018-30-3-417

Abstract

For $\nu \in (0,1)$, the nonautonomous integro-differential equation \[ \mathbf {D}_{t}^{\nu }u-\mathcal {L}_{1}u-\int _{0}^{t}\mathcal {K}_{1}(t-s)\mathcal {L}_{2}u(\cdot ,s)\,ds =f(x,t) \] is considered here, where $\mathbf {D}_{t}^{\nu }$ is the Caputo fractional derivative and $\mathcal {L}_{1}$ and $\mathcal {L}_{2}$ are uniformly elliptic operators with smooth coefficients dependent on time. The global classical solvability of the associated initial-boundary value problems is addressed.

Citation

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Mykola Krasnoschok. Vittorino Pata. Nataliya Vasylyeva. "Solvability of linear boundary value problems for subdiffusion equations with memory." J. Integral Equations Applications 30 (3) 417 - 445, 2018. https://doi.org/10.1216/JIE-2018-30-3-417

Information

Published: 2018
First available in Project Euclid: 8 November 2018

zbMATH: 06979947
MathSciNet: MR3874008
Digital Object Identifier: 10.1216/JIE-2018-30-3-417

Subjects:
Primary: 35C15 , 35R11
Secondary: 45N05

Keywords: Caputo derivatives , coercive estimates , Materials with memory , subdiffusion equations

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

Vol.30 • No. 3 • 2018
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