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Journal of Applied Mathematics and Computing

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07-01-2021 | Original Research

Well-posedness and ill-posedness results for backward problem for fractional pseudo-parabolic equation

Authors: Le Dinh Long, Yong Zhou, Rathinasamy Sakthivel, Nguyen Huy Tuan

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2021

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Abstract

In this paper, we study a pseudo-parabolic equation with the Caputo fractional derivative. By applying the properties of Mittag–Leffler functions and the method of eigenvalue expansion, under a suitable definition of mild solution of our problem, we obtain the existence result and \(L^p\) regularity of the mild solution by using some Sobolev embeddings. Finally, we also give some examples to illustrate the proposed method.

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Title: Well-posedness and ill-posedness results for backward problem for fractional pseudo-parabolic equation
Authors: Le Dinh Long
Yong Zhou
Rathinasamy Sakthivel
Nguyen Huy Tuan
Publication date: 07-01-2021
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2021
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-020-01488-4

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