Local Decay and Asymptotic Profile for the Damped Wave Equation in Asymptotically Euclidean Settings

Explore advanced mathematical research on energy decay for damped wave equations in asymptotically Euclidean settings through this 28-minute conference talk. Discover how the analysis extends beyond optimal decay rates in even dimensions by providing large time asymptotic profiles given by solutions of the free wave equation, while in odd dimensions, learn about improved estimates that surpass decay rates optimal in even dimensions. Examine the mathematical framework that relies on comparing the corresponding resolvent with the resolvent of the free problem for low frequencies, and understand how these results apply to damped wave equations with short-range absorption indices. Gain insights into collaborative research methodology through work conducted jointly with Julien Royer, presented during the thematic meeting on "Wave propagation in guiding structures" at the Centre International de Rencontres Mathématiques in Marseille, France.