Global Existence, Stability and Blow–up of Solutions for p-Biharmonic Hyperbolic Equation with Weak and Strong Damping Terms
In this paper, we study the initial boundary value problem for the following $p$-biharmonic hyperbolic equation with weak and strong damping terms: $$ v_{tt}+\Delta_{p}^{2}v-\mu\Delta_{m}v_{t}+v_{t}=\omega|v|^{k-2}v. $$ Under some assumptions on the initial data, the constants $p,m$ and $k$, we prov...
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| Datum: | 2025 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1100 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | In this paper, we study the initial boundary value problem for the following $p$-biharmonic hyperbolic equation with weak and strong damping terms: $$ v_{tt}+\Delta_{p}^{2}v-\mu\Delta_{m}v_{t}+v_{t}=\omega|v|^{k-2}v. $$ Under some assumptions on the initial data, the constants $p,m$ and $k$, we prove the global existence, stability and blow-up results of solutions. The global solution is obtained by using potential well method and the stability based on Komornik's inequality. We also prove that the solution with negative initial energy blows up in finite and in infinite time.
Mathematical Subject Classification 2020: 35L75, 35A01, 35B35 |
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