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Università degli Studi di Parma Università degli Studi di Parma
University of Parma
Course catalogue
Università degli Studi di Parma
course catalogue

ADVANCED ANALYSIS 2
cod. 23690

Academic year 2008/09
1° year of course - Second semester
Professor
Academic discipline
Analisi matematica (MAT/05)
Field
Formazione analitica
Type of training activity
Characterising
48 hours
of face-to-face activities
6 credits
hub:
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

Aim of the course is to give an overview on the theory of semigroups in Banach spaces and its application in the study of evolution equations of parabolic type

Prerequisites

Spazi di Funzioni

Course unit content

<br />Some results from functional Analysis<br /> <br />Closed and dissipative operators: definitions and main properties<br />Spectrum and resolvent of an operator<br /><br />Strongly continuous semigroups in Banach spaces.<br />Definitions and examples. The infinitesimal generator. Resolvent operator. Hille Yosida Lumer-Phillips theorems<br />Analytic semigroups<br />Sectorial operators and analytic semigroups: definitions and examples. Main properties of analytic semigroups. Interpolation spaces. Asymptotic behaviour of analytic semigroups.<br />Semigroups and evolution equations in Banach spaces<br />The concepts of mild, strong, classical and strict solutions. Spatial and time regularity of the mild solution. Bounded solutions in R^+ and R^-.<br /> 

Full programme

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Bibliography

<br />A. Pazy,  Semigroups of Linear operators and applications to partial differential equations, Springer-Verlag, Berlin, 1983;<br />Notes (by L. Lorenzi, A. Lunardi, G. Metafune, D. Pallara).<br />

Teaching methods

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Assessment methods and criteria

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Other information

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