Prof. Gianmaria Verzini

Argomenti del programma: 1. Real Analysis. Measurable space, measure, outer measure. Generation of an outer measure. Carathéodory's condition, measure induced by an outer measure. Lebesgue's measure on R ^n. Measurable functions. The Lebesgue integral. Abstract integration. Monotone convergence theorem, Fatou's Lemma, Lebesgue's dominated convergence theorem. Comparison between the Lebesgue and Riemann integrals.

Argomenti del programma: 0. Introduction: examples, models and motivations. Pure reaction ODEs systems. 1. Mathematical analysis of the standard model for a single density in a bounded domain. 1.1. Initial value problem (semilinear parabolic equations): well-posedness with Dirichlet, Neumann or Robin boundary conditions; maximum and comparison principles. 1.2.