Attractive models in Astrophysics and Biology : Critical Points and Large Time Asymtotics
type: Dataset
description: In this thesis we study the set of solutions of partial differential equations arising from models in astrophysics and biology. We answer the questions of existence but also we try to describe the behavior of some families of solutions when parameters vary. First we study two problems concerned with astrophysics, where we show the existence of particular sets of solutions depending on a parameter using the Lyapunov-Schmidt reduction method. Afterwards a perturbation argument and Banach's Fixed Point Theorem reduce the original problem to a finite-dimensional one, which can be solved, usually, by variational techniques. The rest of the thesis is de-voted to the study of the Keller-Segel model, which describes the motion of unicellular amoebae. In its simpler version, the Keller-Segel model is a parabolic-elliptic system which shares with some gravitational models the property that interaction is computed through an attractive Poisson / Newton equation. A major difference is the fact that it is set in a two-dimensional setting, which experimentally makes sense, while gravitational models are ordinarily three-dimensional. For this problem the existence issues are well known, but the behaviour of the solutions during the time evolution is still an active area of research. Here we extend properties already known in particular regimes to a broader range of the mass parameter, and we give a precise estimate of the convergence rate of the solution to a known profile as time goes to infinity. This result is achieved using various tools such as symmetrization techniques and optimal functional inequalities. The last chapters deal with numerical results and formal computations related to the Keller-Segel model
identifier: NNT: 2012PA090066
issued: 2026-05-09T18:23:10.546655
language: fr
modified: 2026-05-09T18:23:10.546659
contact point: Organization
  fn: CCSD
keyword: asymptotiques-en-temps-grand
keyword: bubble-tower-solutions
keyword: chemotactisme
keyword: chemotaxis
keyword: continous-stellar-dynamics
keyword: critical-exponent
keyword: developpement-asymptotique
keyword: energie-libre
keyword: entropie-relative
keyword: equation-de-vlasov-poisson
keyword: equilibre-relatif
keyword: exposant-critique
keyword: fonctionnelle-de-lyapunov
keyword: free-energy
keyword: inegalite-logarithmique-de-hardy-littlewood-sobolev
keyword: infoeu-reposemanticsdoctoralthesis
keyword: keller-segel-model
keyword: large-time-asymptotics
keyword: logarithmic-hardy-littlewood-sobolev-inequality
keyword: lyapunov-functional
keyword: lyapunov-schmidt-reduction
keyword: masse-critique
keyword: matched-asymptotics-expansion
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: modele-de-keller-segel
keyword: n-body-problem
keyword: probleme-a-n-corps
keyword: reduction-de-lyapunov-schmidt
keyword: relative-entropy
keyword: relative-equilibrium
keyword: self-similar-solutions
keyword: solutions-auto-similaires
keyword: spectral-gap
keyword: subcritical-mass
keyword: theses
keyword: tour-de-bulles
keyword: trou-spectral
keyword: vlasov-poisson-equation
landing page: https://theses.hal.science/tel-00861568

Attractive models in Astrophysics and Biology : Critical Points and Large Time Asymtotics
type: Distribution
format: HTML
issued: 2026-05-09T18:23:10.549588
modified: 2026-05-09T18:23:10.512708
access URL: https://theses.hal.science/tel-00861568

test_moissonnage_selune
type: Agent