Syllabus
1. Linear semigroups:
- Basic properties of semigroups, generators, resolvent operators; mild solution, variation of parameters
- Hille - Yosida Theorem, Lumer - Phillips Theorem
- Analytic semigroups
- Aplication to parabolic equations 2. Nonlinear application:
- abstract semilinear evolution equation: concept of solution, (local) existence and uniqueness theory, regularity
- concrete examples and their detailed qualitative analysis
Annotation
Strongly continuous semigroup, basic properties, generator, Hille-Yosida Theorem, Lumer-Phillips Theorem, analytic semigroups, applications to evolutionary differential equations. Recommended for master students of mathematical analysis.