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Course, academic year 2019/2020
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Differential equations in Banach spaces - NDIR101
Title in English: Diferenciální rovnice v Banachových prostorech
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2013
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Interchangeability : NMMA440
Is incompatible with: NMMA440
Is interchangeable with: NMMA440
Annotation -
Last update: G_M (13.05.2011)
Theory of linear semigroups (properties of semigroups, generators and resolvent operators, Hille-Yosida theorem, Lumer-Phillips theorem), application to nonlinear partial differential equations.
Literature - Czech
Last update: G_M (21.05.2011)

G.R.Sell, Y.You: Dynamics of Evolutionary Equations, Springer Verlag, New York, 2002

A. Pazy: Semigroups of Linear Operators and Applications to Partial

Differential Equations, Springer-Verlag, New York, 1983

Syllabus - Czech
Last update: G_M (21.05.2011)

1. Lineární semigrupy:

  • Základní vlastnosti semigrupy, generátoru a resolventy, mild řešení,

variace konstant

  • Hille - Yosidova věta, Lumer - Phillipsova věta
  • Analytické semigrupy
  • Perturbační věty
  • Aplikace na parabolické rovnice

2. Nelineární aplikace:

  • Disipativita, asymptotická kompaktnost, globální atraktor.
  • Dimenze atraktoru, exponenciální atraktor, inerciální varieta
  • Aplikace na vybranou (nelineární) rovnici

 
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