Hölder damping for fractional wave equations

2025/10/17 by Jian Wang, Ruoyu Wang, Wang, Jian +1
Engineering · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2510.15213

Abstract

For fractional wave equations with low Hölder regularity damping, we establish quantitative energy decay rates for their solutions when the geometric control condition holds. The energy decay rates depend explicitly on the Hölder regularity of the damping. In particular, we show damping functions with lower Hölder regularities that below a certain threshold give slower energy decay.

Citations

• Optimal backward uniqueness and polynomial stability of second order equations with unbounded damping
• Damping for fractional wave equations and applications to water waves
• Propagation for Schrödinger operators with potentials singular along a hypersurface
• Sharp polynomial decay for polynomially singular damping on the torus
• A Toy Model for Damped Water Waves
• Optimal polynomial decay of functions and operator semigroups
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Related

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• Sharp energy decay rates for the damped wave equation on the torus via non-polynomial derivative bound conditions