| Autor: |
Maes, Frederick, Van Bockstal, Karel |
| Předmět: |
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| Zdroj: |
Fractional Calculus & Applied Analysis; Aug2023, Vol. 26 Issue 4, p1663-1690, 28p |
| Abstrakt: |
In this article, we study the existence and uniqueness of a weak solution to the fractional single-phase lag heat equation. This model contains the terms D t α (∂ t u) and D t α u (with α ∈ (0 , 1) ), where D t α denotes the Caputo fractional differential operator (in time) of order α . We consider homogeneous Dirichlet boundary data for the temperature. We rigorously show the existence of a unique weak solution under low regularity assumptions on the data. Our main strategy is to use the variational formulation and a semidiscretisation in time based on Rothe's method. We obtain a priori estimates on the discrete solutions and show convergence of the Rothe functions to a weak solution. The variational approach is employed to show the uniqueness of this weak solution to the problem. We also consider the one-dimensional problem and derive a representation formula for the solution. We establish bounds on this explicit solution and its time derivative by extending properties of the multivariate Mittag-Leffler function. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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