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Theory of Nonlinear Differential Equations - NDIR064

Title:	Teorie nelineárních diferenciálních rovnic
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014 to 2017
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	http://www.karlin.mff.cuni.cz/~dolejsi/Vyuka/index.htm

Guarantor:	RNDr. Miloslav Vlasák, Ph.D.
Class:	DS, vědecko - technické výpočty
Classification:	Mathematics > Differential Equations, Potential Theory

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: DOLEJSI/MFF.CUNI.CZ (15.04.2008)

The subject of this course is a treatment of nonlinear differential equations. It contains: divergent differential equations, variational methods, applications of theory of monotone and potential operators for elliptic and parabolic equations and numerical methods.

Aim of the course -

Last update: T_KNM (18.05.2008)

Solution of nonlinear elliptic equations in divergence form. Parabolic equations.

Literature -

Last update: T_KNM (18.05.2008)

Fučík Sv., Kufner A.: Nelineární diferenciální rovnice, SNTL, l978

Gajevski H., Gröger K., Zacharias K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, 1974 (překlad do ruštiny 1978)

Zeidler E.: Nonlinear Functional Analysis and its Applications I, II, III (l984, l985, l986)

Teaching methods -

Last update: T_KNM (18.05.2008)

Lectures in a lecture hall.

Requirements to the exam -

Last update: T_KNM (18.05.2008)

Examination according to the syllabus.

Syllabus -

Last update: T_KNM (18.05.2008)

Functional analytical definition of boundary value problems (BVP).

Partial differential equations of second order in a divergence form.

Carathéodory properties.

The Nemytskij operator and its properties.

Variational formulation of boundary value problems.

Application of variational methods and theory of monotone and potential operators for the solution of BVP.

Introduction in the theory of parabolic equations.

Bochner spaces.

Entry requirements -

Last update: T_KNM (18.05.2008)

basic knowledge of functional analysis