Classical solutions for a thin–film equation
Classical solutions for a thin–film equation
View/Type of Scholarly Publication
DissertationDate of Exam
23.11.2007Date of Publication
2008Advisor
Otto, FelixCo-Referee
Koch, HerbertMetadata
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Abstract
The main part of the thesis provides existence, uniqueness and regularity for the 1-d thin-film equation with linear mobility. The equation is viewed as a classical free boundary problem. The focus is laid on the blow up situation near the free boundary. The strategy is based on a priori energy type estimates which provide minimal conditions on the initial data such that a unique global solution exists. As a result, smoothness of the solution is obtained as well as the large time behavior of the free boundary. The second part of the thesis is concerned with Schauder estimates for a related degenerate parabolic linear operator of fourth order. The last part of the thesis provides an optimal lower bound for solutions to 1-d thin-film equations whenever the initial data are almost flat.
Subjects
thin-film equation, degenerate, parabolic, free boundary problem
Classification (DDC)
510 MathematikKnüpfer, Hans: Classical solutions for a thin–film equation. - Bonn, 2008. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-12950
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-12950
@phdthesis{handle:20.500.11811/3558,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-12950,
author = {{Hans Knüpfer}},
title = {Classical solutions for a thin–film equation},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2008,
note = {The main part of the thesis provides existence, uniqueness and regularity for the 1-d thin-film equation with linear mobility. The equation is viewed as a classical free boundary problem. The focus is laid on the blow up situation near the free boundary. The strategy is based on a priori energy type estimates which provide minimal conditions on the initial data such that a unique global solution exists. As a result, smoothness of the solution is obtained as well as the large time behavior of the free boundary. The second part of the thesis is concerned with Schauder estimates for a related degenerate parabolic linear operator of fourth order. The last part of the thesis provides an optimal lower bound for solutions to 1-d thin-film equations whenever the initial data are almost flat.},
url = {https://hdl.handle.net/20.500.11811/3558}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-12950,
author = {{Hans Knüpfer}},
title = {Classical solutions for a thin–film equation},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2008,
note = {The main part of the thesis provides existence, uniqueness and regularity for the 1-d thin-film equation with linear mobility. The equation is viewed as a classical free boundary problem. The focus is laid on the blow up situation near the free boundary. The strategy is based on a priori energy type estimates which provide minimal conditions on the initial data such that a unique global solution exists. As a result, smoothness of the solution is obtained as well as the large time behavior of the free boundary. The second part of the thesis is concerned with Schauder estimates for a related degenerate parabolic linear operator of fourth order. The last part of the thesis provides an optimal lower bound for solutions to 1-d thin-film equations whenever the initial data are almost flat.},
url = {https://hdl.handle.net/20.500.11811/3558}
}
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