Quantitative estimates of $L^p$ maximal regularity for nonautonomous operators and global existence for quasilinear equations - Fédération de Mathématiques de CentraleSupélec Accéder directement au contenu
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.
Fichier principal
Vignette du fichier
main.pdf (538.88 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

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

Identifiants

Citer

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

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More