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Qualitative Aspects of Nonlinear Parabolic Partial Differential Equations and Systems

Petersson, Joakim LU (2005)
Abstract (Swedish)
Popular Abstract in Swedish

Avhandlingen innehåller fyra arbeten om några aspekter på ickelineära paraboliska ekvationer och system.



I det första arbetet presenterar vi ett resultat om "quenching" vid dynamiska randvillkor. Det andra arbetet rör global existens av klassiska lösningar till vissa paraboliska system. I det tredje arbetet bestämmer vi optimala konstanter för vissa Gagliardo-Nirenbergolikheter. Det fjärde arbetet, slutligen, behandlar tidsutvecklingen av extrema för lösningar på obegränsade områden.
Abstract
This thesis contains four papers about some aspects of nonlinear parabolic equations and systems.



Paper 1. A note on quenching for parabolic equations with dynamic boundary conditions



We present a quenching result for semilinear parabolic equations with dynamic boundary conditions in bounded domains with a smooth boundary.



Paper 2. On global existence for semilinear parabolic systems



We present some results on global existence of classical solutions of certain semilinear parabolic systems with homogeneous Dirichlet boundary conditions in bounded domains with a smooth boundary, relaxing the usual monotonicity assumptions on the nonlinearities.



... (More)
This thesis contains four papers about some aspects of nonlinear parabolic equations and systems.



Paper 1. A note on quenching for parabolic equations with dynamic boundary conditions



We present a quenching result for semilinear parabolic equations with dynamic boundary conditions in bounded domains with a smooth boundary.



Paper 2. On global existence for semilinear parabolic systems



We present some results on global existence of classical solutions of certain semilinear parabolic systems with homogeneous Dirichlet boundary conditions in bounded domains with a smooth boundary, relaxing the usual monotonicity assumptions on the nonlinearities.



Paper 3. Best constants for Gagliardo-Nirenberg inequalities on the real line



We use a variational approach to find the best constants for certain Gagliardo-Nirenberg inequalities on the real line. To show the existence of a minimizer, we use the method of concentration-compactness.



Paper 4. On the time evolution of extrema of solutions to nonlinear parabolic equations in unbounded domains



We obtain a result about the time evolution of extrema that can be applied to the study of classical solutions to parabolic equations in unbounded domains with a smooth boundary. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Doc. Molinet, Luc, Paris 13
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Matematik, Mathematics, Optimal constants, Global existence, Parabolic equations, Quenching
pages
42 pages
publisher
Centre for Mathematical Sciences, Lund University
defense location
Sal C, Matematikcentrum,Sölvegatan 18,Lund
defense date
2005-06-03 10:30
ISSN
1404-0034
language
English
LU publication?
yes
id
98431a1d-03a6-4d67-8f26-ab9b22405b59 (old id 544930)
date added to LUP
2007-09-27 16:08:41
date last changed
2016-09-19 08:44:59
@phdthesis{98431a1d-03a6-4d67-8f26-ab9b22405b59,
  abstract     = {This thesis contains four papers about some aspects of nonlinear parabolic equations and systems.<br/><br>
<br/><br>
Paper 1. A note on quenching for parabolic equations with dynamic boundary conditions<br/><br>
<br/><br>
We present a quenching result for semilinear parabolic equations with dynamic boundary conditions in bounded domains with a smooth boundary.<br/><br>
<br/><br>
Paper 2. On global existence for semilinear parabolic systems<br/><br>
<br/><br>
We present some results on global existence of classical solutions of certain semilinear parabolic systems with homogeneous Dirichlet boundary conditions in bounded domains with a smooth boundary, relaxing the usual monotonicity assumptions on the nonlinearities.<br/><br>
<br/><br>
Paper 3. Best constants for Gagliardo-Nirenberg inequalities on the real line<br/><br>
<br/><br>
We use a variational approach to find the best constants for certain Gagliardo-Nirenberg inequalities on the real line. To show the existence of a minimizer, we use the method of concentration-compactness.<br/><br>
<br/><br>
Paper 4. On the time evolution of extrema of solutions to nonlinear parabolic equations in unbounded domains<br/><br>
<br/><br>
We obtain a result about the time evolution of extrema that can be applied to the study of classical solutions to parabolic equations in unbounded domains with a smooth boundary.},
  author       = {Petersson, Joakim},
  issn         = {1404-0034},
  keyword      = {Matematik,Mathematics,Optimal constants,Global existence,Parabolic equations,Quenching},
  language     = {eng},
  pages        = {42},
  publisher    = {Centre for Mathematical Sciences, Lund University},
  school       = {Lund University},
  title        = {Qualitative Aspects of Nonlinear Parabolic Partial Differential Equations and Systems},
  year         = {2005},
}