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

被引：2

作者：

Long, Le Dinh ^{[1
]}

Zhou, Yong ^{[2
,3
]}

Sakthivel, Rathinasamy ^{[4
]}

Tuan, Nguyen Huy ^{[1
,5
]}

机构：

[1] Thu Dau Mot Univ, Div Appl Math, Thu Dau Mot, Binh Duong Prov, Vietnam

[2] Macau Univ Sci & Technol, Fac Informat Technol, Macau 999078, Peoples R China

[3] Xiangtan Univ, Fac Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

[4] Bharathiar Univ, Dept Appl Math, Coimbatore 641046, Tamil Nadu, India

[5] Vietnam Natl Univ, Univ Sci, Fac Math & Comp Sci, 227 Nguyen Van Cu,Dist 5, Ho Chi Minh City, Vietnam

来源：

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2021年 / 67卷 / 1-2期

关键词：

Backward problem; Caputo derivative; pseudo-parabolic equation; Regularity estimates; BOUNDARY-VALUE METHOD; GLOBAL EXISTENCE; BLOW-UP; CAUCHY-PROBLEM;

D O I：

10.1007/s12190-020-01488-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：175 / 206

页数：32

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