Degenerate 3-evolution equations in Gevrey classes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913134145437696 |
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| author | Junior, Alexandre Arias Ascanelli, Alessia |
| author_facet | Junior, Alexandre Arias Ascanelli, Alessia |
| contents | We consider the Cauchy problem for third-order evolution differential operators with variable coefficients, depending on time $t\in [0,T]$ and space $x\in\mathbb{R}$, where the leading coefficient $a_3(t)$ vanishes at $t = 0$ with finite order. We establish sufficient conditions on the behavior of the lower order coefficients $a_j(t,x)$ $j=1,2$ as $t \to 0^{+}$ and $|x| \to \infty$ that ensure well-posedness in $L^2(\mathbb{R})$, $H^{\infty}(\mathbb{R})$ and Gevrey-type spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16576 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Degenerate 3-evolution equations in Gevrey classes Junior, Alexandre Arias Ascanelli, Alessia Analysis of PDEs We consider the Cauchy problem for third-order evolution differential operators with variable coefficients, depending on time $t\in [0,T]$ and space $x\in\mathbb{R}$, where the leading coefficient $a_3(t)$ vanishes at $t = 0$ with finite order. We establish sufficient conditions on the behavior of the lower order coefficients $a_j(t,x)$ $j=1,2$ as $t \to 0^{+}$ and $|x| \to \infty$ that ensure well-posedness in $L^2(\mathbb{R})$, $H^{\infty}(\mathbb{R})$ and Gevrey-type spaces. |
| title | Degenerate 3-evolution equations in Gevrey classes |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.16576 |