Print syllabusTopics in the theory of the heat equation
General data
| Course ID: | 1000-1M23THE |
| Erasmus code / ISCED: |
11.1
|
| Course title: | Topics in the theory of the heat equation |
| Name in Polish: | Topics in the theory of the heat equation |
| Organizational unit: | Faculty of Mathematics, Informatics, and Mechanics |
| Course groups: |
(in Polish) Przedmioty 4EU+ (z oferty jednostek dydaktycznych) Elective courses for 2nd stage studies in Mathematics |
| ECTS credit allocation (and other scores): |
6.00
|
| Language: | English |
| Type of course: | elective monographs |
| Prerequisites (description): | A prospective student should be comfortable with multivariable calculus and analysis in Euclidean spaces. It is advisable but not necessary to have completed a PDE course and a functional analysis course. |
| Mode: | Remote learning |
| Short description: |
The course is dedicated to the study of the heat equation. We will study the key aspects of the heat flow and a range of associated analytical techniques in order to develop an understanding of the heat equation as a canonical model behind a wider variety of linear and non-linear partial differential equations and a useful tool for their analysis. |
| Full description: |
The heat equation is one of the most important objects in the theory of partial differential equations with countless applications to the modeling of real world phenomena. It is also a canonical object that serves as a departure point of a deeper study of more general equations and a testing ground for development of analytical tools. In the standard course of partial differential equations the treatment of the heat flow understandably needs to be abridged to allow for a wealth of other important topics. In this course the heat equation takes center stage. We will cover a range of topics including: - well-posedness: existence, uniqueness and regularity of solutions under variety of assumptions, - smoothing properties of the heat flow, - local and global estimates of solutions, - long time behaviour of solutions, - energy, entropy, Fisher information and elements of the optimal transport theory in the context of the heat flow. |
| Bibliography: |
Material will be taken from a variety of sources including the following books: D.V. Widder - The heat equation, L.C. Evans - Partial differential equations, N.A. Watson - Introduction to heat potential theory and a selection of research papers. |
| Learning outcomes: |
- Student has a working understanding of the fundamentals of the analysis of the heat equation. - Student has an understanding of the key characteristics of the heat flow. - Student has a grasp of the utility the heat equation and its solutions as a tool for more general analytical aims. - Student has an appreciation of the technical complexities introduced by boundary conditions, singularities and forcing terms. |
| Assessment methods and assessment criteria: |
Completion of the course and the final grade will be based on the final project and an overall attendance/performance during the course. |
Classes in period "Summer semester 2023/24" (in progress)
| Time span: | 2024-02-19 - 2024-06-16 |
 
MO TU W WYK
TH FR CW
|
| Type of class: |
Classes, 30 hours
Lecture, 30 hours
|
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| Coordinators: | Mikołaj Sierżęga | |
| Group instructors: | Mikołaj Sierżęga | |
| Students list: | (inaccessible to you) | |
| Examination: | Examination | |
| Course dedicated to a programme: | 4EU+Courses |
|
Copyright by University of Warsaw.
