Well-posedness of damped Kirchhoff-type wave equation with fractional Laplacian
In the present paper, we study the well-posedness of the solution to the initial boundary value problem for the damped Kirchhoff-type wave equation with fractional Laplacian. First, the existence and uniqueness of the local solution are established by the Banach fixed point theorem. Then, the global...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-03-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2023-0172 |
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| author | Chen Shaohua Han Jiangbo Xu Runzhang Yang Chao Zhang Meina |
| author_facet | Chen Shaohua Han Jiangbo Xu Runzhang Yang Chao Zhang Meina |
| author_sort | Chen Shaohua |
| collection | DOAJ |
| description | In the present paper, we study the well-posedness of the solution to the initial boundary value problem for the damped Kirchhoff-type wave equation with fractional Laplacian. First, the existence and uniqueness of the local solution are established by the Banach fixed point theorem. Then, the global existence and finite time blowup of the solution are derived at the subcritical and critical initial energy levels. Finally, the finite time blowup of the solution and upper bound and lower bound estimate of blowup time are given at the arbitrarily positive initial energy level. |
| format | Article |
| id | doaj-art-eba91b405ede42da959e95bcdae1298e |
| institution | Kabale University |
| issn | 2169-0375 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj-art-eba91b405ede42da959e95bcdae1298e2025-08-20T03:58:48ZengDe GruyterAdvanced Nonlinear Studies2169-03752025-03-0125367371810.1515/ans-2023-0172Well-posedness of damped Kirchhoff-type wave equation with fractional LaplacianChen Shaohua0Han Jiangbo1Xu Runzhang2Yang Chao3Zhang Meina4School of Science and Technology, Cape Breton University, Sydney, NSB1P 6L2, CanadaSchool of Mathematical Sciences, Inner Mongolia University, 010021Hohhot, People’s Republic of ChinaCollege of Mathematical Sciences, Harbin Engineering University, 150001Harbin, People’s Republic of ChinaCollege of Mathematical Sciences, Harbin Engineering University, 150001Harbin, People’s Republic of ChinaCollege of Mathematical Sciences, Harbin Engineering University, 150001Harbin, People’s Republic of ChinaIn the present paper, we study the well-posedness of the solution to the initial boundary value problem for the damped Kirchhoff-type wave equation with fractional Laplacian. First, the existence and uniqueness of the local solution are established by the Banach fixed point theorem. Then, the global existence and finite time blowup of the solution are derived at the subcritical and critical initial energy levels. Finally, the finite time blowup of the solution and upper bound and lower bound estimate of blowup time are given at the arbitrarily positive initial energy level.https://doi.org/10.1515/ans-2023-0172kirchhoff-type wave equationfractional laplacianglobal existencefinite time blowupasymptotic behaviorblowup time35r1135l0535a0135b4035b44 |
| spellingShingle | Chen Shaohua Han Jiangbo Xu Runzhang Yang Chao Zhang Meina Well-posedness of damped Kirchhoff-type wave equation with fractional Laplacian Advanced Nonlinear Studies kirchhoff-type wave equation fractional laplacian global existence finite time blowup asymptotic behavior blowup time 35r11 35l05 35a01 35b40 35b44 |
| title | Well-posedness of damped Kirchhoff-type wave equation with fractional Laplacian |
| title_full | Well-posedness of damped Kirchhoff-type wave equation with fractional Laplacian |
| title_fullStr | Well-posedness of damped Kirchhoff-type wave equation with fractional Laplacian |
| title_full_unstemmed | Well-posedness of damped Kirchhoff-type wave equation with fractional Laplacian |
| title_short | Well-posedness of damped Kirchhoff-type wave equation with fractional Laplacian |
| title_sort | well posedness of damped kirchhoff type wave equation with fractional laplacian |
| topic | kirchhoff-type wave equation fractional laplacian global existence finite time blowup asymptotic behavior blowup time 35r11 35l05 35a01 35b40 35b44 |
| url | https://doi.org/10.1515/ans-2023-0172 |
| work_keys_str_mv | AT chenshaohua wellposednessofdampedkirchhofftypewaveequationwithfractionallaplacian AT hanjiangbo wellposednessofdampedkirchhofftypewaveequationwithfractionallaplacian AT xurunzhang wellposednessofdampedkirchhofftypewaveequationwithfractionallaplacian AT yangchao wellposednessofdampedkirchhofftypewaveequationwithfractionallaplacian AT zhangmeina wellposednessofdampedkirchhofftypewaveequationwithfractionallaplacian |