Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Qualitative Properties of Weak Solutions to Partial Differential Equations - NMMA583

Title:	Kvalitativní vlastnosti slabých řešení parciálních diferenciálních rovnic
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
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:	English, Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	https://www2.karlin.mff.cuni.cz/~kaplicky/pages/pages/2020z/nmma583.php
Note:	you can enroll for the course repeatedly

Guarantor:	doc. Mgr. Petr Kaplický, Ph.D. doc. RNDr. Miroslav Bulíček, Ph.D.
Class:	DS, matematické a počítačové modelování DS, matematická analýza M Mgr. MA > Volitelné M Mgr. MOD > Volitelné M Mgr. NVM > Volitelné
Classification:	Mathematics > Differential Equations, Potential Theory
Interchangeability :	NDIR247

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KMA (14.05.2013)

This course is devoted to the classical results about regularity and qualitative properties of weak solutions to partial differential equations and their systems. We assume the knowledge of basic theory of weak solutions to partial differential equations.

Aim of the course -

Last update: T_KMA (13.05.2013)

We intend to pique interest of students in beautiful and difficult branch of mathematics and to learn students some of the classical methods of theory of partial differential equations.

Course completion requirements - Czech

Last update: doc. Mgr. Petr Kaplický, Ph.D. (19.10.2020)

Předmět nemá zápočet. Na konci se skládá zkouška. Zkoušet se bude pouze odpřednesená látka.

Literature

Last update: T_KMA (14.05.2013)

[1] Giaquinta, M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Mathematics Studies 105, Princeton University Press, Princeton, NJ, 1983.

[2] L. C. Evans: Partial regularity for stationary harmonic maps into spheres. Arch. Ration. Mech. Anal. *116*(2), 101-113 (1991).

[3] M. Bulíček and J. Frehse: /C^\alpha regularity for a class of non-diagonal elliptic systems with p-growth/ , Calc. Var. Partial Differential Equations, *43*, No. 3, 441--462, 2012

[4] M. Bulíček, J. Frehse and M. Steinhauer: /Everywhere C^\alpha -estimates for a class of nonlinear elliptic systems with critical growth/, Adv. Calc.Var, online first, 2013

Teaching methods

Last update: doc. Mgr. Petr Kaplický, Ph.D. (05.10.2020)

The course is taught through ZOOM https://cesnet.zoom.us/j/9924525902.

Its webpage is https://www2.karlin.mff.cuni.cz/~kaplicky/pages/pages/2020z/nmma583.php.

Requirements to the exam - Czech

Last update: doc. Mgr. Petr Kaplický, Ph.D. (13.10.2017)

Zkouška bude ústní. Zkoušet budeme látku odpřednesenou na přednášce.

Syllabus

Last update: doc. Mgr. Petr Kaplický, Ph.D. (05.10.2016)

The course has the intention to prepare students for challenges that occur when

instationary PDEs are non-linear. The lecture introduces techniques for existence,

uniqueness and regularity theory which are suitable for non-linear settings; however,

they will be introduced on the most simple model examples. Starting from the

heat equation we will detect fundamental principles and then introduce ways to

generalize these to more sophisticated problems. The generalization shall be made

in accordance to the particular interests of the audience.

Obligatory for the course is the knowledge of the Lebesgue theory of integration.

Some knowledge on weak differentiation and Sobolev spaces is recommended. The

course is intended for Master- and PhD- students that are keen to do research in

mathematics.

Entry requirements

Last update: doc. Mgr. Petr Kaplický, Ph.D. (18.04.2018)

Basic knowledge of weak solutions to PDE's.