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Course, academic year 2018/2019
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Nonlinear Differential Equations and Inequalities 2 - NMMO534
Title in English: Nelineární diferenciální rovnice a nerovnice 2
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:3/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: RNDr. Miroslav Bulíček, Ph.D.
Class: M Mgr. MOD
M Mgr. MOD > Povinně volitelné
Classification: Mathematics > Differential Equations, Potential Theory
Incompatibility : NDIR043
Interchangeability : NDIR043
Annotation -
Last update: T_MUUK (14.05.2013)
Pseudomonotone and monotone operators, set-valued mappings and applications to nonlinear parabolic 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: RNDr. Miroslav Bulíček, Ph.D. (11.06.2019)

The will be an oral exam at the end of the semester. The student should provide the knowledge of the topics presented during the semester. Student will get credits from tutorials provided he actively participated in the tutorials.

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)

Lecture and exercises

Syllabus -
Last update: T_MUUK (14.05.2013)

Continuing the lecture NDIR042, after presentation of auxiliary tools from theory of Bochner spaces of Banach-space valued functions and Aubin-Lions' theorem, it will have analogous structure as the lecture mentioned. Hovewer, beside Galerkin's method, also Rothe's method of semidiscretization in time is presented. Abstract initial-value or periodic problems are applied to initial- (or periodic) boundary-value problems for concrete quasi- or semi-linear parabolic partial differential equations or inequalities. So-called doubly nonlinear problems (i.e. time derivative is involved in a nonlinear manner) are addressed, too.

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