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Some examples causing energy growth for solutions to wave equations. (English) Zbl 1235.35188

Summary: We study energy growth for solutions to wave equations. We prove that there exist compact in space perturbations of the wave equation \(\partial_{t}^{2}u-\Delta u=0\) such that the energy of solution grows at the rate \(\exp((1+t)^{\alpha})\) for any \(\alpha \geq 0\).

MSC:

35L15 Initial value problems for second-order hyperbolic equations
35L05 Wave equation
35B40 Asymptotic behavior of solutions to PDEs
Full Text: DOI

References:

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