We prove results of well-posedness of the global Cauchy problem in Sobolev spaces for a class of evolution equations with real characteristics that contains an Euler– Bernoulli vibrating beam model. We consider non-Lipschitz coefficients with respect to the time variable t and study the sharp rate of their oscillations. This is coupled with some necessary decay conditions as the spatial variable x → ∞.
On Schrödinger type evolution equations with non-Lipschitz coefficients / M. Cicognani; M. Reissig. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 190:(2011), pp. 645-665. [10.1007/s10231-010-0167-9]
On Schrödinger type evolution equations with non-Lipschitz coefficients
CICOGNANI, MASSIMO;
2011
Abstract
We prove results of well-posedness of the global Cauchy problem in Sobolev spaces for a class of evolution equations with real characteristics that contains an Euler– Bernoulli vibrating beam model. We consider non-Lipschitz coefficients with respect to the time variable t and study the sharp rate of their oscillations. This is coupled with some necessary decay conditions as the spatial variable x → ∞.File in questo prodotto:
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