Lecturer:
Course Type:
PhD Course
Academic Year:
2022-2023
Duration:
32 h
Description:
- Bochner integral; Pettis and Bochner theorems; vector valued distributions and Sobolev functions.
- Elements on unbounded operators: closed, dissipative and maximal dissipative operators.
- Semigroups and their generators.
- Cauchy problem for abstract equations, Duhamel formula.
- Hille-Yosida, Lumer-Phillips and Stone theorems, construction of (semi)groups associated to Heat, Wave, Klein Gordon and Schrödinger equations.
- Semilinear abstract problem, local solution, extension, global solution, continuous dependence on data.
- Special properties of Heat semigroup.
- Example of a nonlinear problem for Klein-Gordon equation.
- Elements of interpolation theory (Three Lines and Riesz-Thorin theorem) and application to the Cauchy problem for nonlinear Schrödinger via contraction mapping theorem.
- Conservation laws.
- Global solutions, continuous dependence on data.
Research Group:
Location:
A-133