On the principle of linearized stability for quasilinear evolution equations in time-weighted spaces

2024/12/18 by Bogdan–Vasile Matioc, Matioc, Bogdan-Vasile, Lina Sophie Schmitz +3 · 2 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods for differential equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2412.13940

openalex publication_date 2024/12/18 · openalex created_date 2024/12/21 · openalex updated_date 2026/07/28

Abstract

Quasilinear (and semilinear) parabolic problems of the form v'=A(v)v+f(v) with strict inclusion dom(f)\subsetneq dom(A) of the domains of the function v↦ f(v) and the quasilinear part v↦ 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 dom(f) and 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.

Cited by

• Dynamics of the reversible Gray-Scott model and convergence to its irreversible limit
• Asymptotic stability of solutions to semilinear evolution equations in Banach spaces

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