Global existence and nonexistence of semilinear wave equation with a new condition
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866909097832480768 |
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| author | Sabitbek, Bolys |
| author_facet | Sabitbek, Bolys |
| contents | In this paper, we consider the initial-boundary problem for semilinear wave equation with a new condition $$α\int_0^{u } f(s)ds \leq uf(u) + βu^2 +ασ,$$ for some positive constants $α$, $β$, and $σ$, where $β< \frac{λ_1(α-2)}{2}$ with $λ_1$ being a first eigenvalue of Laplacian. By introducing a family of potential wells, we establish the invariant sets, vacuum isolation of solutions, global existence and blow-up solutions of semilinear wave equation for initial conditions $E(0)<d$ and $E(0)=d$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2111_11334 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Global existence and nonexistence of semilinear wave equation with a new condition Sabitbek, Bolys Analysis of PDEs 35K71, 35B44, 35A01 In this paper, we consider the initial-boundary problem for semilinear wave equation with a new condition $$α\int_0^{u } f(s)ds \leq uf(u) + βu^2 +ασ,$$ for some positive constants $α$, $β$, and $σ$, where $β< \frac{λ_1(α-2)}{2}$ with $λ_1$ being a first eigenvalue of Laplacian. By introducing a family of potential wells, we establish the invariant sets, vacuum isolation of solutions, global existence and blow-up solutions of semilinear wave equation for initial conditions $E(0)<d$ and $E(0)=d$. |
| title | Global existence and nonexistence of semilinear wave equation with a new condition |
| topic | Analysis of PDEs 35K71, 35B44, 35A01 |
| url | https://arxiv.org/abs/2111.11334 |