ADVANCED ANALYSIS 2
Learning outcomes of the course unit
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
Spazi di Funzioni
Course contents summary
Some results from functional Analysis
Closed and dissipative operators: definitions and main properties
Spectrum and resolvent of an operator
Strongly continuous semigroups in Banach spaces.
Definitions and examples. The infinitesimal generator. Resolvent operator. Hille Yosida Lumer-Phillips theorems
Sectorial operators and analytic semigroups: definitions and examples. Main properties of analytic semigroups. Interpolation spaces. Asymptotic behaviour of analytic semigroups.
Semigroups and evolution equations in Banach spaces
The concepts of mild, strong, classical and strict solutions. Spatial and time regularity of the mild solution. Bounded solutions in R^+ and R^-.
A. Pazy, Semigroups of Linear operators and applications to partial differential equations, Springer-Verlag, Berlin, 1983;
Notes (by L. Lorenzi, A. Lunardi, G. Metafune, D. Pallara).