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Pré-Publication, Document De Travail Année : 2024

Quantitative estimates of $L^p$ maximal regularity for nonautonomous operators and global existence for quasilinear equations

Résumé

In this work, we obtain quantitative estimates of the continuity constant for the $L^p$ maximal regularity of relatively continuous nonautonomous operators $\mathbb{A} : I \longrightarrow \mathcal{L}(D,X)$, where $D \subset X$ densely and compactly. They allow in particular to establish a new general growth condition for the global existence of strong solutions of Cauchy problems for nonlocal quasilinear equations for a certain class of nonlinearities $u \longrightarrow \mathbb{A}(u)$. The estimates obtained rely on the precise asymptotic analysis of the continuity constant with respect to perturbations of the operator of the form $\mathbb{A}(\cdot) + \lambda I$ as $\lambda \longrightarrow \pm \infty$. A complementary work in preparation supplements this abstract inquiry with an appli- cation of these results to nonlocal parabolic equations in noncylindrical domains depending on the time variable.
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Dates et versions

hal-04484486 , version 1 (29-02-2024)
hal-04484486 , version 2 (11-03-2024)

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Théo Belin, Pauline Lafitte. Quantitative estimates of $L^p$ maximal regularity for nonautonomous operators and global existence for quasilinear equations. 2024. ⟨hal-04484486v2⟩
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