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In this paper, we consider one-dimensional wave equation with real-valued square-summable
potential. We establish the long-time asymptotics of solutions by, first, studying the
stationary problem and, second, using the spectral representation for the evolution
equation. In particular, we prove that part of the wave travels ballistically if
q ∈ L2(ℝ+) and this result is
sharp.
We investigate a generalized class of fractional hemivariational inequalities involving the time-fractional aspect. The existence result is established by employing the Rothe method in conjunction with the surjectivity of multivalued pseudomonotone operators and the properties of the Clarke generalized gradient. We are also exploring a numerical approach to address the problem, utilizing both spatially semi-discrete and fully discrete finite elements, along with a discrete approximation of the fractional...
L’equazione in condizioni di debole iperbolicità , è ben posta negli spazi di Gevrey con , purché sia di Gevrey in di ordine e risulti
We prove that the Cauchy problem for a class of hyperbolic equations with non-Lipschitz coefficients is well-posed in and in Gevrey spaces. Some counter examples are given showing the sharpness of these results.
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