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 I x R^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.

Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems / Addona, Davide; Angiuli, Luciana; Lorenzi, Luca Francesco Giuseppe. - In: ADVANCES IN NONLINEAR ANALYSIS. - ISSN 2191-9496. - 8:1(2019), pp. 225-252. [10.1515/anona-2016-0166]

Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems

ADDONA, DAVIDE;ANGIULI, Luciana;LORENZI, Luca Francesco Giuseppe
2019

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 I x R^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.
Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems / Addona, Davide; Angiuli, Luciana; Lorenzi, Luca Francesco Giuseppe. - In: ADVANCES IN NONLINEAR ANALYSIS. - ISSN 2191-9496. - 8:1(2019), pp. 225-252. [10.1515/anona-2016-0166]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2825381
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