Differential equations in Banach spaces - NDIR101

• Title: Diferenciální rovnice v Banachových prostorech
• Guaranteed by: Department of Mathematical Analysis (32-KMA)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2022
• Semester: summer
• E-Credits: 3
• Hours per week, examination: summer s.:2/0, Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: cancelled
• Language: Czech
• Teaching methods: full-time
• 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

English

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.

Czech

Last update: G_M (13.05.2011)

Teorie lineárních semigrup (vlastnosti semigrupy, generátoru a rezolventy, Hille-Yosidova věta, Lumer-Phillipsova věta), aplikace na nelineární parciální diferenciální rovnice.

Literature

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

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