The aim of the course consists in illustrating the semigroup theory and its application to the study of Cauchy problems associated to partial differential equations of parabolic type.
1. Bounded and strongly continuous semigroups.
2. Sectorial operators.
3. Generation of analytic semigroups by differential operators.
4. Intermediate spaces.
5. Nonhomogeneous problems.
6. Asymptotic behaviour in linear problems.
7. Nonlinear problems.
8. Behaviour near stationary solutions.
K. Engel, R. Nagel: One parameter semigroups for linear evolution equations, Springer-Verlag, Berlin, 1999
A. Lunardi: Analytic semigroups and optimal regularity in parabolic problems, Birkhauser, Basel, 1995.
Lectures, assigned exercises
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