Journal of Integral Equations and Applications

Solvability of linear boundary value problems for subdiffusion equations with memory

Mykola Krasnoschok, Vittorino Pata, and Nataliya Vasylyeva

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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.

Article information

J. Integral Equations Applications, Volume 30, Number 3 (2018), 417-445.

First available in Project Euclid: 8 November 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R11: Fractional partial differential equations 35C15: Integral representations of solutions
Secondary: 45N05: Abstract integral equations, integral equations in abstract spaces

Materials with memory subdiffusion equations Caputo derivatives coercive estimates


Krasnoschok, Mykola; Pata, Vittorino; Vasylyeva, Nataliya. Solvability of linear boundary value problems for subdiffusion equations with memory. J. Integral Equations Applications 30 (2018), no. 3, 417--445. doi:10.1216/JIE-2018-30-3-417.

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