Solvability of pseudoparabolic equation with Caputo fractional derivative

S.E. Aitzhanov, U.R. Kusherbayeva and K.S. Bekenayeva

Chaos, Solitons & Fractals, 2022, vol. 160, issue C

Abstract: This paper is devoted to the study of solvability of the problem for a pseudo-parabolic equation with a Caputo fractional derivative. The existence of the weak solution is investigated by applying Galerkin approximations and a priori estimates. On the way to prove the weak solution's uniqueness of the problem the Sobolev embedding theorem, Rellich-Kondrashov theorem and Gronwall-Bellman Lemma are applied. Along with this, the blow up of the solution to the problem in finite time is proved. The global solvability of the initial boundary value problem and the uniqueness of the weak generalized solution have been studied.

Keywords: Pseudoparabolic equation; Caputo fractional derivative; Galerkin approximations; Weak solution; Blow up of solution; Global solvability (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004039

DOI: 10.1016/j.chaos.2022.112193

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