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Article Dans Une Revue Annales Henri Lebesgue Année : 2023

BOUNDED WEAK SOLUTIONS TO A CLASS OF DEGENERATE CROSS-DIFFUSION SYSTEMS

Résumé

Bounded weak solutions are constructed for a degenerate parabolic system with a full diffusion matrix, which is a generalized version of the thin film Muskat system. Boundedness is achieved with the help of a sequence $(\mathcal{E}_n)_{n\ge 2}$ of Liapunov functionals such that $\mathcal{E}_n$ is equivalent to the $L_n$-norm for each $n \ge 2$ and $\mathcal{E}_n^{1/n}$ controls the $L_\infty$-norm in the limit $n\to\infty$. Weak solutions are built by a compactness approach, special care being needed in the construction of the approximation in order to preserve the availability of the above-mentioned Liapunov functionals.
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Dates et versions

hal-03528167 , version 1 (17-01-2022)

Identifiants

Citer

Philippe Laurençot, Bogdan-Vasile Matioc. BOUNDED WEAK SOLUTIONS TO A CLASS OF DEGENERATE CROSS-DIFFUSION SYSTEMS. Annales Henri Lebesgue, 2023, 6, pp.847--874. ⟨10.5802/ahl.179⟩. ⟨hal-03528167⟩
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