The Cauchy Problem For Quasi-Linear Parabolic Systems Revisited
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917228827377664 |
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| author | Gallagher, Isabelle Moussa, Ayman |
| author_facet | Gallagher, Isabelle Moussa, Ayman |
| contents | We study a class of parabolic quasilinear systems, in which the diffusion matrix is not uniformly elliptic, but satisfies a Petrovskii condition of positivity of the real part of the eigenvalues. Local well-posedness is known since the work of Amann in the 90s, by a semi-group method. We first revisit these results in the context of Sobolev spaces modelled on $L^2$ and then explore the endpoint Besov case $B_{p,1}^{d/p}$. We also exemplify our method on the SKT system, showing the existence of local, non-negative, strong solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Cauchy Problem For Quasi-Linear Parabolic Systems Revisited Gallagher, Isabelle Moussa, Ayman Analysis of PDEs We study a class of parabolic quasilinear systems, in which the diffusion matrix is not uniformly elliptic, but satisfies a Petrovskii condition of positivity of the real part of the eigenvalues. Local well-posedness is known since the work of Amann in the 90s, by a semi-group method. We first revisit these results in the context of Sobolev spaces modelled on $L^2$ and then explore the endpoint Besov case $B_{p,1}^{d/p}$. We also exemplify our method on the SKT system, showing the existence of local, non-negative, strong solutions. |
| title | The Cauchy Problem For Quasi-Linear Parabolic Systems Revisited |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.08226 |