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arXiv · 1607.05247

Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems

Davide Addona·Luciana Angiuli·Luca Lorenzi
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Abstract

We study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over R^d and in L^p-spaces with respect to tight evolution systems of measures. Here, the linear part of the equation is a nonautonomous second-order elliptic operator with unbounded coefficients defined in IxR^d, (I being a right-halfline). To the above Cauchy problem we associate a nonlinear evolution operator, which we study in detail, proving some summability improving properties. We also study the stability of the null solution to the Cauchy problem.

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Davide Addona, Luciana Angiuli, Luca Lorenzi. 2016-07-18. Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems. https://arxiv.org/abs/1607.05247

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