Self-similar solutions to the porous medium equation

Title

Self-similar solutions to the porous medium equation

 Author

Vural, Asya (TU Delft Electrical Engineering, Mathematics and Computer Science)

Contributor

Gnann, M.V. (mentor) ORCID 0000-0002-1479-0387
Dubbeldam, J.L.A. (graduation committee) ORCID 0000-0002-5891-998X

 Degree granting institution

Delft University of Technology

 Programme

Applied Mathematics

 Date

2021-08-09

 Abstract

The porous medium equation $\dv{t}u=\dv{x}(k(u)\dv{x}u)$ is a non-linear degenerate parabolic partial differential equation. Consequently, existence and uniqueness of its solutions is not immediately evident.
This bachelor thesis presents a detailed discussion of Atkinson's and Peletier's 1971 article ``Similarity profiles of flows through porous media" on existence and uniqueness of self-similar solutions to the porous medium equation.
First, in chapter 2 the general version of the porous medium equation along with some applications will be discussed. Then, in chapter 3 the proofs and statements of the Picard-Lindelöf theorem, Peano's existence theorem and Gronwall's inequality will be presented. These standard theorems concern differential equations and will be used in the next chapter. Finally, in chapter 4 Atkinson's and Peletier's article will be worked out in detail.

 Subject

porous media
porous medium equation
Partial Differential Equations
self-similar solutions
Fluid dynamics

 To reference this document use:

http://resolver.tudelft.nl/uuid:5ea1f8c9-69a4-4a12-b0e0-b498da3db398

 Part of collection

Student theses

 Document type

bachelor thesis

 Rights

© 2021 Asya Vural
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