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Dettagli Bibliografici
Autori principali: Matioc, Bogdan-Vasile, Schmitz, Lina Sophie, Walker, Christoph
Natura: Preprint
Pubblicazione: 2024
Soggetti:
Accesso online:https://arxiv.org/abs/2412.13940
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Sommario:
  • Quasilinear (and semilinear) parabolic problems of the form $v'=A(v)v+f(v)$ with strict inclusion $\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the function $v\mapsto f(v)$ and the quasilinear part $v\mapsto A(v)$ are considered in the framework of time-weighted function spaces. This allows one to establish the principle of linearized stability in intermediate spaces lying between $\mathrm{dom}(f)$ and $\mathrm{dom}(A)$ and yields a greater flexibility with respect to the phase space for the evolution. In applications to differential equations such intermediate spaces may correspond to critical spaces exhibiting a scaling invariance. Several examples are provided to demonstrate the applicability of the results.