M9150 Partial Differential Equations II

Faculty of Science
Autumn 2002
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Kolář, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D.
Prerequisites
M8110 Partial Differential Equations I
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
This course is a continuation of Partial differential equations I. The aim of the first part is to give a broader view on solutions of pde's and their properties, using modern methods. The main tools are functional and Fourier analysis. The aim of the second part is to show on the example of Navier-Stokes equations some techniques for analysis of nonlinear equations and their systems.
Syllabus
  • 1. Modern methods - Sobolev spaces of generalized functions - Weak formulation of elliptic problems - Lax-Milgram lemma and existence of solutions - Variational formulation of elliptical problems - Ritz-Galerkin method - Monotone operators 2. Navier-Stokes equations - Examples of exact solutions - Vorticity, vorticity equation - Leray's formulation - Properties of 2-D flows - Beltrami flow
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
Assessment methods (in Czech)
Typ výuky - přednáška a cvičení, zkouška - ústní
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.
  • Enrolment Statistics (Autumn 2002, recent)
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