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Course, academic year 2018/2019
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Nonlinear Differential Equations and Inequalities for Ph.D. Students II - NMMO622
Title in English: Nelineární diferenciální rovnice a nerovnice pro doktorandy II
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 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: DS, matematické a počítačové modelování
DS, matematická analýza
Classification: Mathematics > Mathematical Modeling in Physics
Incompatibility : NDIR143
Interchangeability : NDIR143
Annotation -
Last update: G_M (07.05.2014)
Pseudomonotone and monotone operators, set-valued mappings and applications to nonlinear parabolic partial differential equations and inequalities.
Aim of the course -
Last update: G_M (07.05.2014)

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.

Literature - Czech
Last update: G_M (07.05.2014)

T.Roubíček: Nonlinear Partial Differential Equations with Applications. Birkhauser, Basel, 2005.

Teaching methods -
Last update: G_M (07.05.2014)


Syllabus -
Last update: G_M (07.05.2014)

Continuing the lecture NDIR142, 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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