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• W2952657917 abstract "In this paper we investigate the following fractional order in time Cauchy problem begin{equation*} begin{cases} mathbb{D}_{t}^{alpha }u(t)+Au(t)=f(u(t)), & 1<alpha <2, u(0)=u_{0},,,,u^{prime }(0)=u_{1}. & end{cases}% end{equation*}% The fractional in time derivative is taken in the classical Caputo sense. In the scientific literature such equations are sometimes dubbed as fractional-in time wave equations or super-diffusive equations. We obtain results on existence and regularity of local and global weak solutions assuming that $A$ is a nonnegative self-adjoint operator with compact resolvent in a Hilbert space and with a nonlinearity $fin C^{1}({mathbb{R}}% )$ that satisfies suitable growth conditions. Further theorems on the existence of strong solutions are also given in this general context." @default.
• W2952657917 created "2019-06-27" @default.
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• W2952657917 date "2018-08-07" @default.
• W2952657917 modified "2023-10-03" @default.
• W2952657917 title "Well-posedness results for a class of semi-linear super-diffusive equations" @default.
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• W2952657917 hasPublicationYear "2018" @default.
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