The Cauchy problem for quasi-linear parabolic systems revisited Article Swipe
Isabelle Gallagher
,
Ayman Moussa
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5802/jep.319
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5802/jep.319
We study a class of parabolic quasilinear systems, in which the diffusion matrix is not uniformly elliptic, but satisfies the Petrovskii condition (positivity of eigenvalues’ real part). 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 and then explore the endpoint Besov case . We also exemplify our method on the SKT system, showing the existence of local, non-negative, strong solutions.
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- en
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- https://doi.org/10.5802/jep.319
- https://jep.centre-mersenne.org/item/10.5802/jep.319.pdf
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- 27
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- 10
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https://openalex.org/W4400518512Canonical identifier for this work in OpenAlex
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The Cauchy problem for quasi-linear parabolic systems revisitedWork title
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articleOpenAlex work type
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enPrimary language
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2025Year of publication
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2025-10-15Full publication date if available
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Isabelle Gallagher, Ayman MoussaList of authors in order
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https://doi.org/10.5802/jep.319Publisher landing page
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https://jep.centre-mersenne.org/item/10.5802/jep.319.pdfDirect link to full text PDF
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diamondOpen access status per OpenAlex
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https://jep.centre-mersenne.org/item/10.5802/jep.319.pdfDirect OA link when available
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0Total citation count in OpenAlex
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