紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2012, 49(4), p. 1065-1085

NOTE ON LOWER BOUNDS OF ENERGY GROWTH FOR SOLUTIONS TO WAVE EQUATIONS

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2012-12

In this note we study lower bounds of energy growth for solutions to wave equations which are compact in space perturbations of the wave equation ∂^2_tu−Δu=0. Assuming that there exists a null bicharacteristic (x(t),ξ(t)), parametrized by the time t, such that x(t) remains inside a ball and ξ(t) outside a ball for t≥0 we prove that the solution operator R(t) is bounded from below by constant times √<｜ξ(t)｜/｜ξ(0)｜> in the operator norm. We apply this result to examples constructed by the same idea as in Colombini and Rauch [1] and show that there exist compact in space perturbations which cause exp(ct^α) growth of the energy for any given 0≤α≤1.

10.18910/23423

23423

NOTE ON LOWER BOUNDS OF ENERGY GROWTH FOR SOLUTIONS TO WAVE EQUATIONS

Osaka University and Osaka City University, Departments of Mathematics

英語

2012-12

Osaka Journal of Mathematics

49

4

1065

1085

https://hdl.handle.net/11094/23423

10.18910/23423

https://doi.org/10.18910/23423