## Note on lower bounds of energy growth for solutions to wave equations.(English)Zbl 1273.35069

The model is a compact in space perturbation of the wave equation. The solution operator is denoted with $$R(t,0)$$ and an upper bound on the growth of its norm is shown. Further, assuming the existence of some special null bicharacteristics, lower bounds for the norm of $$R(t,0)$$ are proved. The obtained result is applied to wave equations constructed by means of techniques developed in [F. Colombini and J. Rauch, J. Reine Angew. Math. 616, 1–14 (2008; Zbl 1158.35012)].

### MSC:

 35B45 A priori estimates in context of PDEs 35L20 Initial-boundary value problems for second-order hyperbolic equations 35B40 Asymptotic behavior of solutions to PDEs

### Keywords:

null bicharacteristic

Zbl 1158.35012
Full Text:

### References:

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