Theo Belin, Pauline Lafitte
Abstract:
In this work, we obtain quantitative estimates of the continuity constant
for the \(L^p\) maximal regularity of relatively continuous nonautonomous
operators \(A : I \to \mathcal{L}(D,X)\), where \(D \hookrightarrow X\) 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
\(u \mapsto \mathbb{A}(u)\). The estimates obtained rely on the precise
asymptotic analysis of the continuity constant with respect to
perturbations of the operator of the form \(A(\cdot) + \lambda \text{Id}\) as
\(\lambda \to \pm \infty\). A complementary work in preparation supplements
this abstract inquiry with an application of these results to nonlocal
parabolic equations in noncylindrical domains depending on the time
variable.
Submitted October 8, 2024. Published February 26, 2025
Math Subject Classifications: 35K90, 35K59, 35D35, 47D06.
Key Words: Nonautonomous Cauchy problem; \(L^p\) maximal regularity; relatively continuous operators; quasilinear equations.
DOI: 10.58997/ejde.2025.18
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| Théo Belin Université Paris-Saclay Laboratoire MICS, Centrale Supélec, France email: theo.belin@centralesupelec.fr |
| Pauline Lafitte Université Paris-Saclay Fédération de Mathématiques de Centrale Supélec (FR CNRS 3487), France email: pauline.lafitte@centralesupelec.fr |
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