Damped wave equations on compact hyperbolic surfaces

2017/12/07 by Jin, Long
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1712.02692

Abstract

We prove exponential decay of energy for solutions of the damped wave equation on compact hyperbolic surfaces with regular initial data as long as the damping is nontrivial. The proof is based on a similar strategy as in Dyatlov-Jin and in particular, uses the fractal uncertainty principle proved in Bourgain-Dyatlov.

Related

• Asymptotic stability of the wave equation on compact surfaces and locally distributed damping - A sharp result
• Sharp energy decay rates for the damped wave equation on the torus via non-polynomial derivative bound conditions
• Energy decay for the time dependent damped wave equation
• Wave Decay with Singular Damping
• Long time energy averages and a lower resolvent estimate for damped waves