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Course, academic year 2023/2024
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Nonlinear differential equations - NMNV406
Title: Nelineární diferenciální rovnice
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. Mgr. Petr Knobloch, Dr., DSc.
Class: M Mgr. NVM > Povinné
Classification: Mathematics > Differential Equations, Potential Theory, Numerical Analysis
Is interchangeable with: NMNV402
Annotation -
Last update: doc. RNDr. Václav Kučera, Ph.D. (05.12.2018)
The subject is the solution of nonlinear differential equations in divergence form, the definition of weak solutions, theorems dealing with the existence and uniqueness of the solution using the theory of monotone operators, numerical solution using finite element methods including the discretization and solution of the arising algebraic equations.
Literature - Czech
Last update: doc. RNDr. Václav Kučera, Ph.D. (15.01.2019)

L. C. Evans: Partial Differential Equations, AMS, 2010.

E. Zeidler: Nonlinear Functional Analysis and its Applications II/A, Springer, 1990.

V. Dolejší, K. Najzar: Nelineární funkcionální analýza, 2011, skripta MFF UK, 202 s. ISBN 978-80-7378-137-8

S. Fučík, A. Kufner: Nelineární diferenciální rovnice, 1978, SNTL, 344 s.

Syllabus -
Last update: doc. RNDr. Václav Kučera, Ph.D. (05.12.2018)

Basic theorems from the theory of monotone and potential operators.

Nonlinear differential equations in divergent form.

Carathéodory's growth conditions, Nemycky operators. Variational methods and aplication of theory of monotone and potential operator, proof of existence of solution.

Numerical solution of nonlinear differential equations using the finite element method.

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