Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay
We study the Euler-Bernoulli equations with time delay: utt+Δ2u−g1∗Δ2u+g2∗Δu+μ1ut(x,t)∣ut(x,t)∣m−2+μ2ut(x,t−τ)∣ut(x,t−τ)∣m−2=f(u),{u}_{tt}+{\Delta }^{2}u-{g}_{1}\ast {\Delta }^{2}u+{g}_{2}\ast \Delta u+{\mu }_{1}{u}_{t}\left(x,t){| {u}_{t}\left(x,t)| }^{m-2}+{\mu }_{2}{u}_{t}\left(x,t-\tau ){| {u}_{...
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De Gruyter
2025-02-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2024-0124 |
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| author | Lin Rongrui Gao Yunlong She Lianbing |
| author_facet | Lin Rongrui Gao Yunlong She Lianbing |
| author_sort | Lin Rongrui |
| collection | DOAJ |
| description | We study the Euler-Bernoulli equations with time delay: utt+Δ2u−g1∗Δ2u+g2∗Δu+μ1ut(x,t)∣ut(x,t)∣m−2+μ2ut(x,t−τ)∣ut(x,t−τ)∣m−2=f(u),{u}_{tt}+{\Delta }^{2}u-{g}_{1}\ast {\Delta }^{2}u+{g}_{2}\ast \Delta u+{\mu }_{1}{u}_{t}\left(x,t){| {u}_{t}\left(x,t)| }^{m-2}+{\mu }_{2}{u}_{t}\left(x,t-\tau ){| {u}_{t}\left(x,t-\tau )| }^{m-2}=f\left(u), where τ\tau represents the time delay. We exhibit the blow-up behavior of solutions with both positive and nonpositive initial energy for the Euler-Bernoulli equations involving time delay. |
| format | Article |
| id | doaj-art-4a7c2b30a880487882c042e6eac2a974 |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-4a7c2b30a880487882c042e6eac2a9742025-02-10T13:24:36ZengDe GruyterOpen Mathematics2391-54552025-02-0123137238810.1515/math-2024-0124Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delayLin Rongrui0Gao Yunlong1She Lianbing2School of Mathematics and Statistics, Liupanshui Normal University, Liupanshui, Guizhou 553004, P. R. ChinaSchool of Mathematics and Statistics, Liupanshui Normal University, Liupanshui, Guizhou 553004, P. R. ChinaSchool of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui 236037, P. R. ChinaWe study the Euler-Bernoulli equations with time delay: utt+Δ2u−g1∗Δ2u+g2∗Δu+μ1ut(x,t)∣ut(x,t)∣m−2+μ2ut(x,t−τ)∣ut(x,t−τ)∣m−2=f(u),{u}_{tt}+{\Delta }^{2}u-{g}_{1}\ast {\Delta }^{2}u+{g}_{2}\ast \Delta u+{\mu }_{1}{u}_{t}\left(x,t){| {u}_{t}\left(x,t)| }^{m-2}+{\mu }_{2}{u}_{t}\left(x,t-\tau ){| {u}_{t}\left(x,t-\tau )| }^{m-2}=f\left(u), where τ\tau represents the time delay. We exhibit the blow-up behavior of solutions with both positive and nonpositive initial energy for the Euler-Bernoulli equations involving time delay.https://doi.org/10.1515/math-2024-0124euler-bernoulli equationblow-upnonlinear time delay35l0535b4493d15 |
| spellingShingle | Lin Rongrui Gao Yunlong She Lianbing Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay Open Mathematics euler-bernoulli equation blow-up nonlinear time delay 35l05 35b44 93d15 |
| title | Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay |
| title_full | Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay |
| title_fullStr | Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay |
| title_full_unstemmed | Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay |
| title_short | Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay |
| title_sort | blow up of solutions for euler bernoulli equation with nonlinear time delay |
| topic | euler-bernoulli equation blow-up nonlinear time delay 35l05 35b44 93d15 |
| url | https://doi.org/10.1515/math-2024-0124 |
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