Anomalous pseudo-parabolic Kirchhoff-type dynamical model
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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-10-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2021-0207 |
| _version_ | 1811280167618740224 |
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| author | Dai Xiaoqiang Han Jiangbo Lin Qiang Tian Xueteng |
| author_facet | Dai Xiaoqiang Han Jiangbo Lin Qiang Tian Xueteng |
| author_sort | Dai Xiaoqiang |
| collection | DOAJ |
| description | 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(u0) ⩽ d, respectively. In particular, the lower and upper bound estimates of the blowup time are given for J(u0)<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. |
| first_indexed | 2024-04-13T01:08:52Z |
| format | Article |
| id | doaj.art-67f3aa31ee28411b966370f542969cd5 |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-04-13T01:08:52Z |
| publishDate | 2021-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-67f3aa31ee28411b966370f542969cd52022-12-22T03:09:15ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2021-10-0111150353410.1515/anona-2021-0207Anomalous pseudo-parabolic Kirchhoff-type dynamical modelDai Xiaoqiang0Han Jiangbo1Lin Qiang2Tian Xueteng3Department of Electronic Information, Jiangsu University of Science and Technology, Jiangsu212003, P.R. ChinaCollege of Mathematical Sciences, Harbin Engineering University, Harbin150001, P.R. ChinaCollege of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin150001, P.R. ChinaCollege of Mathematical Sciences, Harbin Engineering University, Harbin150001, P.R. ChinaIn 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(u0) ⩽ d, respectively. In particular, the lower and upper bound estimates of the blowup time are given for J(u0)<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.https://doi.org/10.1515/anona-2021-0207pseudo-parabolic kirchhoff-type equationglobal existenceasymptotic behaviorblowup35b4035r1135k55 |
| spellingShingle | Dai Xiaoqiang Han Jiangbo Lin Qiang Tian Xueteng Anomalous pseudo-parabolic Kirchhoff-type dynamical model Advances in Nonlinear Analysis pseudo-parabolic kirchhoff-type equation global existence asymptotic behavior blowup 35b40 35r11 35k55 |
| title | Anomalous pseudo-parabolic Kirchhoff-type dynamical model |
| title_full | Anomalous pseudo-parabolic Kirchhoff-type dynamical model |
| title_fullStr | Anomalous pseudo-parabolic Kirchhoff-type dynamical model |
| title_full_unstemmed | Anomalous pseudo-parabolic Kirchhoff-type dynamical model |
| title_short | Anomalous pseudo-parabolic Kirchhoff-type dynamical model |
| title_sort | anomalous pseudo parabolic kirchhoff type dynamical model |
| topic | pseudo-parabolic kirchhoff-type equation global existence asymptotic behavior blowup 35b40 35r11 35k55 |
| url | https://doi.org/10.1515/anona-2021-0207 |
| work_keys_str_mv | AT daixiaoqiang anomalouspseudoparabolickirchhofftypedynamicalmodel AT hanjiangbo anomalouspseudoparabolickirchhofftypedynamicalmodel AT linqiang anomalouspseudoparabolickirchhofftypedynamicalmodel AT tianxueteng anomalouspseudoparabolickirchhofftypedynamicalmodel |