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Course, academic year 2023/2024
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Differential Equations in Banach Spaces - NMMA440
Title: Diferenciální rovnice v Banachových prostorech
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 4
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: taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Tomáš Bárta, Ph.D.
doc. RNDr. Dalibor Pražák, Ph.D.
Class: M Mgr. MA
M Mgr. MA > Povinně volitelné
Classification: Mathematics > Differential Equations, Potential Theory
Incompatibility : NDIR101
Interchangeability : NDIR101
Is interchangeable with: NDIR101
Annotation -
Last update: T_KMA (02.05.2013)
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.
Literature -
Last update: T_KMA (02.05.2013)

G.R.Sell, Y. You: Dynamics of evolutionary equations, Springer 2002.

A. Pazy: Semigroups of linear operators and applications to partial differential equations , Springer 1983.

Requirements to the exam -
Last update: doc. RNDr. Tomáš Bárta, Ph.D. (28.10.2019)

Regular submitting homeworks is required, they can replace the final exam.

Syllabus -
Last update: T_KMA (06.05.2015)

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

Entry requirements -
Last update: doc. RNDr. Dalibor Pražák, Ph.D. (01.05.2018)

Basic concepts from functional analysis (Banach space, operator, norm). Basic theory of ODEs.

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