Final value problem governed by a class of time-space fractional pseudo-parabolic equations with weak nonlinearities

被引：1

作者：

Dinh Ke, Tran ^{[1
]}

Bao Ngoc, Tran ^{[2
]}

Huy Tuan, Nguyen ^{[3
,4
]}

机构：

[1] Hanoi Natl Univ Educ, Dept Math, Hanoi, Vietnam

[2] Karl Franzens Univ Graz, Inst Math & Sci Comp, Graz, Austria

[3] Van Lang Univ, Sci & Technol Adv Inst, Div Appl Math, Ho Chi Minh City, Vietnam

[4] Van Lang Univ, Fac Appl Technol, Sch Technol, Ho Chi Minh City, Vietnam

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 06期

关键词：

final value problem; fractional pseudo-parabolic equation; fractional Sobolev space; Hilbert scale; weak nonlinearity; well-posedness; GLOBAL EXISTENCE; BLOW-UP; MODEL;

D O I：

10.1002/mma.9866

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the final value problem involving a class of semilinear fractional pseudo-parabolic equations, where the nonlinearity probably takes values in fractional Sobolev spaces. By establishing some estimates for resolvent operators and employing the embedding related to Hilbert scales and fractional Sobolev spaces, we are able to obtain the existence and uniqueness result to the mentioned problem. In addition, the behavior of solutions at initial time is analyzed with respect to the final data. It will be shown that various cases of the nonlinearity functions meet our setting, including functions with gradient term.

引用

页码：5307 / 5328

页数：22

共 46 条

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