Partial differential equations and their applications 1000-1D09RC

We will cover methods used to study partial differential equations. They include:
-- variational methods applicable to elliptic equations,
-- monotonicity methods applicable to parabolic equations,
-- Galerkin method applied to Navier - Stokes equation,
-- the method of characteristics applied to hyperbolic equation,
-- the semigroup method applied to infinite dimensional dynamical systems.

Term 2025:

In the year 2025/6 the central topics of the seminar are:
1) the notion of the gradient flow for variatinal functionals. Selected examples include the evolutionary p-harmonic equation.
2) investigation of the convergence of the flows, this includes that energy dissipation balance;
3) the notion of Gamma-convergence of gradient flows;
4) variational inequalities.

Type of course

Master's seminars

Prerequisites (description)

Functional analysis I 1000-135AF1, Analytic functions 1000-134FAN, Probability II 1000-135RP2, Qualitative theory of ordinary differential equations 1000-135RRJ or Partial differential equations I 1000-135RC1a

Course coordinators

Term 2024:

Piotr Gwiazda
Agnieszka Świerczewska-Gwiazda

Term 2025:

Piotr Rybka
Anna Zatorska-Goldstein

Bibliography

A part of these topics can be found in the book by L.C.Evans, The Partial Differential Equations

Additional information

Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:

Master's degree, second cycle programme, Mathematics

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 1000-1D09RC in USOSweb