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Semigroup theory and applications

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.
Location: 
A-133
Next Lectures: 

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