On the blow-up for a Kuramoto-Velarde type equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917599550373888 |
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| author | Jarrin, Oscar Vergara-Hermosilla, Gaston |
| author_facet | Jarrin, Oscar Vergara-Hermosilla, Gaston |
| contents | It is known that the Kuramoto-Velarde equation is globally well-posed on Sobolev spaces in the case when the parameters $γ_1$ and $γ_2$ involved in the non-linear terms verify $ γ_1=\frac{γ_1}{2}$ or $γ_2=0$. In the complementary case of these parameters, the global existence or blow-up of solutions is a completely open (and hard) problem. Motivated by this fact, in this work we consider a non-local version of the Kuramoto-Velarde equation. This equation allows us to apply a Fourier-based method and, within the framework $γ_2\neq \frac{γ_1}{2}$ and $γ_2\neq 0$, we show that large values of these parameters yield a blow-up in finite time of solutions in the Sobolev norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the blow-up for a Kuramoto-Velarde type equation Jarrin, Oscar Vergara-Hermosilla, Gaston Analysis of PDEs It is known that the Kuramoto-Velarde equation is globally well-posed on Sobolev spaces in the case when the parameters $γ_1$ and $γ_2$ involved in the non-linear terms verify $ γ_1=\frac{γ_1}{2}$ or $γ_2=0$. In the complementary case of these parameters, the global existence or blow-up of solutions is a completely open (and hard) problem. Motivated by this fact, in this work we consider a non-local version of the Kuramoto-Velarde equation. This equation allows us to apply a Fourier-based method and, within the framework $γ_2\neq \frac{γ_1}{2}$ and $γ_2\neq 0$, we show that large values of these parameters yield a blow-up in finite time of solutions in the Sobolev norm. |
| title | On the blow-up for a Kuramoto-Velarde type equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.17619 |