Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems

Advances in Nonlinear Analysis

article

Davide Addona¹  Luciana Angiuli²  Luca Lorenzi¹ 

[1] Dipartimento di Scienze Matematiche, Università degli Studi di Parma;Dipartimento di Matematica e Fisica, Università del Salento

关键词: Nonautonomous second-order elliptic operators;    semilinear parabolic equations;    unbounded coefficients;    hypercontractivity;    supercontractivity;    ultraboundedness;    stability;   

DOI  :  10.1515/anona-2016-0166

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over ℝ d {\mathbb{R}^{d}} and in L p {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 × ℝ d {I\times\mathbb{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.

【 授权许可】

CC BY