Solvability of pseudoparabolic equation with Caputo fractional derivative
Aitzhanov S.E. Kusherbayeva U.R. Bekenayeva K.S.
July 2022Elsevier Ltd
Chaos, Solitons and Fractals
2022#160
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 solutions 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.
Blow up of solution , Caputo fractional derivative , Galerkin approximations , Global solvability , Pseudoparabolic equation , Weak solution
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Al-Farabi Kazakh National University, Almaty, Kazakhstan
International University of Information Technologies, Almaty, Kazakhstan
Abai Kazakh National Pedagogical University, Almaty, Kazakhstan
Al-Farabi Kazakh National University
International University of Information Technologies
Abai Kazakh National Pedagogical University
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