Anomalous pseudo-parabolic Kirchhoff-type dynamical model-Reference-Cited by-同舟云学术

Anomalous pseudo-parabolic Kirchhoff-type dynamical model

Published:2021-10-04 Issue:1 Volume:11 Page:503-534
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Dai Xiaoqiang¹,Han Jiangbo²,Lin Qiang³⁴,Tian Xueteng²⁵

Affiliation:

1. Department of Electronic Information, Jiangsu University of Science and Technology , Jiangsu , P.R. China

2. College of Mathematical Sciences, Harbin Engineering University , Harbin , P.R. China

3. College of Intelligent Systems Science and Engineering, Harbin Engineering University , Harbin , P.R. China

4. Department of Mathematics, University of Craiova , Craiova , Romania

5. College of Teacher Education, Quzhou University , Quzhou , P.R. China

Abstract

Abstract In this paper, we study an anomalous pseudo-parabolic Kirchhoff-type dynamical model aiming to reveal the control problem of the initial data on the dynamical behavior of the solution in dynamic control system. Firstly, the local existence of solution is obtained by employing the Contraction Mapping Principle. Then, we get the global existence of solution, long time behavior of global solution and blowup solution for J(u 0) ⩽ d, respectively. In particular, the lower and upper bound estimates of the blowup time are given for J(u 0)<d. Finally, we discuss the blowup of solution in finite time and also estimate an upper bound of the blowup time for high initial energy.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anona-2021-0207/pdf

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