Problèmes aux limites pour les équations de Hamilton-Jacobi avec viscosité et données initiales peu régulières

Abstract : This thesis deal with the viscous Hamilton-Jacobi equations (VHJ) on bounded domains with smooth boundary. This equation is a nonlinear parabolic problem for which the second term is a power of the gradient of the solution. We study the existence, uniqueness and regularity of weak solutions for (VHJ) equation with Dirichlet or Neumann homogeneous boundary conditions and irregular initial data .The cases of initial data a bounded Radon measure, or a measurable function in the Lebesgue space are investigated. Next, using the Bernstein technique we prove some qualitative properties of these solutions. A particular attention is given to the long time behaviour depending on the sign and the exponent of the nonlinear term.
Document type :
Theses
Complete list of metadatas

Cited literature [81 references]  Display  Hide  Download

https://hal.univ-lorraine.fr/tel-01748137
Contributor : Thèses Ul <>
Submitted on : Thursday, March 29, 2018 - 11:26:14 AM
Last modification on : Thursday, April 12, 2018 - 1:59:12 AM
Long-term archiving on: Friday, September 14, 2018 - 12:15:13 AM

File

SCD_T_2003_0058_DABULEANU.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : tel-01748137, version 1

Collections

Citation

Simona Dabuleanu. Problèmes aux limites pour les équations de Hamilton-Jacobi avec viscosité et données initiales peu régulières. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2003. Français. ⟨NNT : 2003NAN10058⟩. ⟨tel-01748137⟩

Share

Metrics

Record views

21

Files downloads

28