Exponential growth for the wave equation with compact time‐periodic positive potential |
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| Authors: | Ferruccio Colombini Jeffrey Rauch Vesselin Petkov |
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| Institution: | 1. Università di Pisa, Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56127, Italy;2. University of Michigan, Department of Mathematics, 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109‐1043;3. Université Bordeaux 1, Institut de Mathématiques, Bat A33, 351 cours de la Libération, F‐33405 Talence, France |
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| Abstract: | We prove the existence of smooth positive potentials V(t, x), periodic in time and with compact support in x, for which the Cauchy problem for the wave equation utt ? Δxu + V(t, x)u = 0 has solutions with exponentially growing global and local energy. Moreover, we show that there are resonances, z ∈ ?, |z| > 1, associated to V(t, x). © 2008 Wiley Periodicals, Inc. |
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