Sumários
Lesson no. 26: Evolution Problems, part IV
29 Maio 2018, 14:00 • Hugo Tavares
The Hille-Yosida theorem (conclusion). Applications to the heat and wave equation.
Lesson no. 25: Evolution Problems, part III
25 Maio 2018, 11:00 • Hugo Tavares
The abstract Cauchy problem. The resolvent. Hille-Yosida theorem and Yosida approximation
Exercise class 13
24 Maio 2018, 11:00 • Hugo Tavares
The Hille-Yosida Theorem and applications.
Solution of exercises 1 and 2 of Exercise sheet 9.
Lesson 24: Evolution Problems, part II
22 Maio 2018, 14:00 • Hugo Tavares
Evolution Problems: the case of bounded operators (the exponential).
Definition of semigroup; contraction semigroups. The infinitesimal operator of a semigroup: differentiable properties, general properties.
Lesson 23: Elliptic Problems, part IV. Evolution Problems, part I
18 Maio 2018, 11:00 • Hugo Tavares
Conclusion of the H^2-regularity for ellitpic problems. Higher interior regularity. Global regularity and application to the study of a 4th order problem.
Evolution Problems: motivations and abstract Cauchy Problem. Preliminaries on functions with values in Banach spaces (continuity, differentiability, integration).