Global solutions and blow-up for the wave equation with variable coefficients: II. boundary supercritical source
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909129117794304 |
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| author | Ha, Tae Gab |
| author_facet | Ha, Tae Gab |
| contents | In this paper, we consider the wave equation with variable coefficients and boundary damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy depending on the growth near zero on the damping term. Moreover, we prove the blow-up of the weak solution with positive initial energy as well as nonpositive initial energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15897 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global solutions and blow-up for the wave equation with variable coefficients: II. boundary supercritical source Ha, Tae Gab Analysis of PDEs In this paper, we consider the wave equation with variable coefficients and boundary damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy depending on the growth near zero on the damping term. Moreover, we prove the blow-up of the weak solution with positive initial energy as well as nonpositive initial energy. |
| title | Global solutions and blow-up for the wave equation with variable coefficients: II. boundary supercritical source |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2306.15897 |