Blow-up analysis of a nonlinear pseudo-parabolic equation with memory term
This paper deals with the blow-up phenomena for a nonlinear pseudo-parabolic equation with a memory term $u_{t}-\triangle{u}-\triangle{u}_{t}+\int_{0}^{t}g(t-\tau)\triangle{u}(\tau)d\tau=|{u}|^{p}{u}$ in a bounded domain, with the initial and Dirichlet boundary conditions. We first obtain the finite...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020220/fulltext.html |
| _version_ | 1818295664292921344 |
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| author | Huafei Di Yadong Shang Jiali Yu |
| author_facet | Huafei Di Yadong Shang Jiali Yu |
| author_sort | Huafei Di |
| collection | DOAJ |
| description | This paper deals with the blow-up phenomena for a nonlinear pseudo-parabolic equation with a memory term $u_{t}-\triangle{u}-\triangle{u}_{t}+\int_{0}^{t}g(t-\tau)\triangle{u}(\tau)d\tau=|{u}|^{p}{u}$ in a bounded domain, with the initial and Dirichlet boundary conditions. We first obtain the finite time blow-up results for the solutions with initial data at non-positive energy level as well as arbitrary positive energy level, and give some upper bounds for the blow-up time $T^{*}$ depending on the sign and size of initial energy $E(0)$. In addition, a lower bound for the life span $T^{*}$ is derived by means of a differential inequality technique if blow-up does occur. |
| first_indexed | 2024-12-13T03:51:14Z |
| format | Article |
| id | doaj.art-95b1532dd0d7485aa4bebdf5f23265de |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-13T03:51:14Z |
| publishDate | 2020-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-95b1532dd0d7485aa4bebdf5f23265de2022-12-22T00:00:42ZengAIMS PressAIMS Mathematics2473-69882020-04-01543408342210.3934/math.2020220Blow-up analysis of a nonlinear pseudo-parabolic equation with memory termHuafei Di0Yadong Shang1Jiali Yu21 School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong, 510006, P. R. China1 School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong, 510006, P. R. China2 School of Science, Dalian Jiaotong University, Dalian, Liaoning, 116028, P. R. ChinaThis paper deals with the blow-up phenomena for a nonlinear pseudo-parabolic equation with a memory term $u_{t}-\triangle{u}-\triangle{u}_{t}+\int_{0}^{t}g(t-\tau)\triangle{u}(\tau)d\tau=|{u}|^{p}{u}$ in a bounded domain, with the initial and Dirichlet boundary conditions. We first obtain the finite time blow-up results for the solutions with initial data at non-positive energy level as well as arbitrary positive energy level, and give some upper bounds for the blow-up time $T^{*}$ depending on the sign and size of initial energy $E(0)$. In addition, a lower bound for the life span $T^{*}$ is derived by means of a differential inequality technique if blow-up does occur.https://www.aimspress.com/article/10.3934/math.2020220/fulltext.htmlpseudo-parabolic equationmemory termblow upupper boundlower bound |
| spellingShingle | Huafei Di Yadong Shang Jiali Yu Blow-up analysis of a nonlinear pseudo-parabolic equation with memory term AIMS Mathematics pseudo-parabolic equation memory term blow up upper bound lower bound |
| title | Blow-up analysis of a nonlinear pseudo-parabolic equation with memory term |
| title_full | Blow-up analysis of a nonlinear pseudo-parabolic equation with memory term |
| title_fullStr | Blow-up analysis of a nonlinear pseudo-parabolic equation with memory term |
| title_full_unstemmed | Blow-up analysis of a nonlinear pseudo-parabolic equation with memory term |
| title_short | Blow-up analysis of a nonlinear pseudo-parabolic equation with memory term |
| title_sort | blow up analysis of a nonlinear pseudo parabolic equation with memory term |
| topic | pseudo-parabolic equation memory term blow up upper bound lower bound |
| url | https://www.aimspress.com/article/10.3934/math.2020220/fulltext.html |
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