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Semilinear nonautonomous parabolic equations with unbounded coefficients in the linear part

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2015年 125卷 468-497页

作者： Angiuli, Luciana Lunardi, Alessandra Univ Salento Dipartimento Matemat & Fis Ennio De Giorgi I-73100 Lecce Italy Univ Parma Dipartimento Matemat & Informat I-43124 Parma Italy

We study the Cauchy problem for the semilinear nonautonomous parabolic equation u(t) = A(t)u +psi(t, u) in [s, tau] x R-d, tau > s, in the spaces C-b ([s, tau] x R-d) and in L-p((s, tau) x R-d,nu). Here. is a Borel measure defined via a tight evolution system of measures for the evolution operator G(t, s) associated to the family of time depending second order uniformly elliptic operators A(t). Sufficient conditions for existence in the large and stability of the null solution are also given in both Cb and Lp contexts. The novelty with respect to the literature is that the coefficients of the operators A(t) are allowed to be unbounded. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： nonautonomous second-order elliptic operators Semilinear parabolic equations Unbounded coefficients Stability

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On the Dirichlet and Neumann Evolution operators in

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POTENTIAL ANALYSIS 2014年第4期41卷 1079-1110页

作者： Angiuli, Luciana Lorenzi, Luca Univ Parma Dipartimento Matemat & Informat I-43124 Parma Italy

We prove some uniform and pointwise gradient estimates for the Dirichlet and the Neumann evolution operators and associated with a class of nonautonomous elliptic operators (t) with unbounded coefficients defined in Ix (where I is a right-halfline or I=a"e). We also prove the existence and the uniqueness of a tight evolution system of measures associated with , which turns out to be sub-invariant for , and we study the asymptotic behaviour of the evolution operators and in the L (p) -spaces related to the system {mu(N)(t)}(t is an element of I).

关键词： nonautonomous second-order elliptic operators Unbounded coefficients Evolution operators Pointwise and uniform gradient estimates Evolution systems of measures Asymptotic behaviour

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Compactness and invariance properties of evolution operators associated with Kolmogorov operators with unbounded coefficients

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2011年第1期379卷 125-149页

作者： Angiuli, Luciana Lorenzi, Luca Univ Parma Dipartimento Matemat I-43124 Parma Italy Univ Salento Dipartimento Matemat Ennio De Giorgi I-73100 Lecce Italy

In this paper we consider nonautonomous elliptic operators A with nontrivial potential term defined in I x R-d. where I is a right-halfline (possibly I = R). We prove that we can associate an evolution operator (G (t, s)) with A in the space of all bounded and continuous functions on R-d. We also study the compactness properties of the operator G(t, s). Finally. we provide sufficient conditions guaranteeing that each operator G(t, s) preserves the usual L-p-spaces and C-0(R-d). (C) 2010 Elsevier Inc. All rights reserved.

关键词： nonautonomous second-order elliptic operators Unbounded coefficients Evolution operators Compactness Invariant subspaces

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