On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding

2022/03/07 by Giuliano Lazzaroni, Riccardo Molinarolo, Lazzaroni, Giuliano +5 · 1 citation
Earth and Planetary Sciences · Engineering · #35L05 #35L85 #35Q74 #35R37 #74H20 #74K35 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Ocean Waves and Remote Sensing #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2203.03738

openalex publication_date 2022/03/07 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We revisit some issues about existence and regularity for the wave equation in noncylindrical domains. Using a method of diffeomorphisms, we show how, through increasing regularity assumptions, the existence of weak solutions, their improved regularity and an energy balance can be derived. As an application, we give a rigorous definition of dynamic energy release rate density for some problems of debonding, and we formulate a proper notion of solution for such problems. We discuss the consistence of such formulation with previous ones, given in literature for particular cases.

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• Controllability of a One-Dimensional Dynamic Debonding Model

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