Stabilization for the wave equation with fully subciritical logarithmic nonlinearity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910051983163392 |
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| author | Ha, Tae Gab |
| author_facet | Ha, Tae Gab |
| contents | In this paper, we consider a wave equation with strong damping and logarithmic nonlinearity. This paper aims to study the local and global existence, uniqueness and the uniform energy decay rate of a weak solution under some sufficient conditions on the initial data. Unlike previous literature restricted to the lower subcritical range $2 < γ< \frac{2(n-1)}{n-2}$, we successfully extend the validity of the well-posedness and stabilization results to the upper subcritical range $\frac{2(n-1)}{n-2} \leq γ< \frac{2n}{n-2}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_13179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stabilization for the wave equation with fully subciritical logarithmic nonlinearity Ha, Tae Gab Analysis of PDEs 35L05, 35A01, 35A02, 35B35 In this paper, we consider a wave equation with strong damping and logarithmic nonlinearity. This paper aims to study the local and global existence, uniqueness and the uniform energy decay rate of a weak solution under some sufficient conditions on the initial data. Unlike previous literature restricted to the lower subcritical range $2 < γ< \frac{2(n-1)}{n-2}$, we successfully extend the validity of the well-posedness and stabilization results to the upper subcritical range $\frac{2(n-1)}{n-2} \leq γ< \frac{2n}{n-2}$. |
| title | Stabilization for the wave equation with fully subciritical logarithmic nonlinearity |
| topic | Analysis of PDEs 35L05, 35A01, 35A02, 35B35 |
| url | https://arxiv.org/abs/2603.13179 |