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Analytic Semigroups and Optimal Regularity in Parabolic Problems
Introduction.- 0 Preliminary material: spaces of continuous and Holder continuous functions.- 1 Interpolation theory.- Analytic semigroups and intermediate spaces.- 3 Generation of analyticExpand
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On the Ornstein-Uhlenbeck Operator in Spaces of Continuous Functions
We study the realization of the Ornstein-Uhlenbeck operator A in the space of the uniformly continuous and bounded functions in Rn. We prove that it generates a semigroup which is neither stronglyExpand
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On the linear heat equation with fading memory
The linear heat equation in materials with memory is studied by reducing it to an abstract Volterra equation. Results of regularity, asymptotic behavior, and positivity are given.
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Averaging Principle for Nonautonomous Slow-Fast Systems of Stochastic Reaction-Diffusion Equations: The Almost Periodic Case
We study the validity of an averaging principle for a slow-fast system of stochastic reaction-diffusion equations. We assume here that the coefficients of the fast equation depend on time, so thatExpand
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  • Open Access
Abstract quasilinear parabolic equations
On considere des problemes paraboliques quasi lineaires abstraits (P 0 ):u'(t)=A(t,u(t)) u(t)+f(t,u(t)), t>0, U(o)=u 0 ou u(t) est une fonction a valeurs dans un espace de Banach X. On donne desExpand
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Functional Analytic Methods for Evolution Equations
Preface.- Giuseppe Da Prato: An Introduction to Markov Semigroups.- Peer C. Kunstmann and Lutz Weis: Maximal$L_p -regularity for Parabolic Equations, Fourier Multiplier Theorems and $H^\inftyExpand
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Solvability on the real line of a class of linear volterra integrodifferential equations of parabolic type
SummaryWe consider an abstract parabolic integrodifferential equation with infinite delay in general Banach space X:(*) $$u'(t) = Au(t) + \int\limits_{ - \infty }^t {K(t - s)u(s)ds + f(t),t \in R}$$Expand
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Schauder estimates for a class of degenerate elliptic and parabolic operators with unbounded coefficients in R
L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditionsExpand
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  • Open Access
Ornstein–Uhlenbeck operators with time periodic coefficients
Abstract.We study the realization of the differential operator $$u \mapsto u_t - L(t)u$$ in the space of continuous time periodic functions, and in L2 with respect to its (unique) invariantExpand
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We study a class of elliptic operators A with unbounded coeffi- cients defined in I × R d for some unbounded interval IR. We prove that, for any s 2 I, the Cauchy problem u(s,·) = f 2 Cb(R d ) forExpand
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  • Open Access