Global existence for a fractionally damped nonlinear Jordan--Moore--Gibson--Thompson equation

2025/07/02 by Meliani, Mostafa, Said-Houari, Belkacem
#35B25 #35L75 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.01538

Abstract

In nonlinear acoustics, higher-order-in-time equations arise when taking into account a class of thermal relaxation laws in the modeling of sound wave propagation. In the literature, these families of equations came to be known as Jordan--Moore--Gibson--Thompson (JMGT) models. In this work, we show the global existence of solutions relying only on minimal assumptions on the nonlocal damping kernel. In particular, our result covers the until-now open question of global existence of solutions for the fractionally damped JMGT model with quadratic gradient nonlinearity. The factional damping setting forces us to work with non-integrable kernels, which require a tailored approach in the analysis to control. This approach relies on exploiting the specific nonlinearity structure combined with a weak damping provided by the nonlocality kernel.

Citations

• Well-posedness and global extensibility criteria for time-fractionally damped Jordan--Moore--Gibson--Thompson equation
• Energy decay of some multi-term nonlocal-in-time Moore--Gibson--Thompson equations
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• Time-fractional Moore-Gibson-Thompson equations
• Parabolic approximation of quasilinear wave equations with applications in nonlinear acoustics
• On the Jordan-Moore-Gibson-Thompson equation: well-posedness with\n quadratic gradient nonlinearity and singular limit for vanishing relaxation\n time
• Optimal decay estimates for time-fractional and other non-local subdiffusion equations via energy methods
• Linear Models of Dissipation whose Q is almost Frequency Independent--II

Related

• Well-posedness and global extensibility criteria for time-fractionally damped Jordan--Moore--Gibson--Thompson equation
• The vanishing relaxation time behavior of multi-term nonlocal Jordan-Moore-Gibson-Thompson equations
• On the Jordan-Moore-Gibson-Thompson equation: well-posedness with\n quadratic gradient nonlinearity and singular limit for vanishing relaxation\n time
• A unified analysis framework for generalized fractional Moore--Gibson--Thompson equations: Well-posedness and singular limits
• Nonlinear acoustic equations of fractional higher order at the singular limit