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Course, academic year 2023/2024

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Nonlinear Differential Equations and Inequalities 1 - NMMO533

Title:	Nelineární diferenciální rovnice a nerovnice 1
Guaranteed by:	Mathematical Institute of Charles University (32-MUUK)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:3/1, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Miroslav Bulíček, Ph.D.
Class:	M Mgr. MOD M Mgr. MOD > Povinně volitelné
Classification:	Mathematics > Differential Equations, Potential Theory
Incompatibility :	NDIR042
Interchangeability :	NDIR042
Is interchangeable with:	NDIR042

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Annotation -

Last update: T_MUUK (14.05.2013)

Pseudomonotone and monotone operators, set-valued mappings and applications to nonlinear elliptic partial differential equations and inequalities.

Aim of the course -

Last update: T_MUUK (14.05.2013)

To present at least a bit of Nonlinear Differential Equations and Inequalities

Course completion requirements -

Last update: doc. RNDr. Miroslav Bulíček, Ph.D. (04.10.2018)

Students must obtain credicts from tutorials, credits are obtained by participation at the tutorilas. The exam has the oral form and is based on the lectures.

Literature -

Last update: T_MUUK (14.05.2013)

T.Roubíček: Nonlinear differenctial equations with applications. Birkhauser, Basel, 2005.

Teaching methods -

Last update: T_MUUK (14.05.2013)

Lectures and exercises

Requirements to the exam -

Last update: doc. RNDr. Miroslav Bulíček, Ph.D. (04.10.2018)

The exam is based on the lectures.

Syllabus -

Last update: T_MUUK (14.05.2013)

The goal is a presentation of fundamental techniques used for nonlinear differential equations and inequalities both on the level of abstract mappings in Banach spaces and on the typical cases derived as weak formulations of steady-state boundary-value or unilateral problems or free-boundary problems for quasi- or semi-linear elliptic partial differential equations. In particular, methods of monotonicity and compactness, variational methods for problem with (possibly nonsmooth) potentials, Galerkin's method, and the penalty method will be addressed, as well as systems of nonlinear differential equations with definite applications in (thermo)mechanics of continua or other areas of physics.

Exercises will involve modifications of problems presented in the main course.

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