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Course, academic year 2018/2019
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Nonlinear Differential Equations and Inequalities for Ph.D. Students I - NMMO621
Title in English: Nelineární diferenciální rovnice a nerovnice pro doktorandy I
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: 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 : NDIR142
Interchangeability : NDIR142
Annotation -
Last update: G_M (07.05.2014)
Pseudomonotone and monotone operators, set-valued mappings and applications to nonlinear elliptic 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. (04.10.2018)

The exam has the oral form and is based on the lectures.

Literature - Czech
Last update: G_M (07.05.2014)

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

Teaching methods -
Last update: G_M (07.05.2014)

Lecture

Requirements to the exam -
Last update: RNDr. Miroslav Bulíček, Ph.D. (04.10.2018)

There will be an oral exam. The exam is based on the lectures.

Syllabus -
Last update: G_M (07.05.2014)

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.

Entry requirements -
Last update: RNDr. Miroslav Bulíček, Ph.D. (04.10.2018)

Basic knowledge of theory of weak solutions to linear elliptic equations.

 
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