# Evolution problems associated to the p-Laplace operator : asymptotic behavior and nonexistence

Abstract : This thesis is dedicated to the study of two subjects in the field of evolution problems associated with the $p$-Laplace operator. The first subject is concerned with the study of long time behavior of bounded solutions and the second subject is devoted to the study of nonexistence of positive nontrivial solutions. The first chapter of this thesis is devoted to a general introduction to the p-Laplace operator and a résumé of this thesis. The first chapter is written in French. Chapter 2 is dedicated to the study of convergence as the time $t\to+\infty$ of bounded solutions of evolution problems associated with the p-Laplace operator on a bounded interval with homogeneous Dirichlet, Neumann, or Robin boundary conditions converges. The results of Chapter 2 are contained in article \cite{hauer-convergence-2012}, which was published in the journal « Nonlinear Differential Equations and Applications NoDea ». Chapter 3 is devoted to the study of nonexistence of positive nontrivial weak solutions of parabolic equations associated to the p-Laplace operator with a convection term and a singular potential. The results of Section 3.2 and Section 3.4.1 of Chapter 3 are contained in article \cite{Hauer:2012fk}, which was accepted for publication in the journal « Archiv der Mathematik ». The results of Section 3.4.2 of Chapter 3 are not yet published
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Theses
File URL :
http://docnum.univ-lorraine.fr/prive/DDOC_T_2012_0269_HAUER.pdf

https://hal.univ-lorraine.fr/tel-01749393
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Submitted on : Thursday, March 29, 2018 - 12:15:07 PM
Last modification on : Thursday, February 25, 2021 - 10:50:04 AM

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• HAL Id : tel-01749393, version 1

### Citation

Daniel Hauer. Evolution problems associated to the p-Laplace operator : asymptotic behavior and nonexistence. General Mathematics [math.GM]. Université de Lorraine, 2012. English. ⟨NNT : 2012LORR0269⟩. ⟨tel-01749393⟩

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