Exponential growth of the local energy for moving obstacles
Georgi S. Popov, Tsviatko Rangelov · Osaka City University (Osaka City University) · 1989
We study the wave equation in the exterior of a moving obstacle. Our body may move or change its shape smoothly, as long as it remains in a fixed sphere and moves slower than the wave speed. We investigate the local energy when t→∞. For periodically moving obstacles we find some conditions on the boundary Σ which guarantee the existence of initial data such that the local energy grows exponentially. We also consider motions of Σ which are not periodic in time. If the body expands whenever a fixed trapping ray hits the boundary we prove that the local energy is not bounded in time