Attractive models in Astrophysics and Biology : Critical Points and Large Time Asymtotics
type: Dataset
contact point: Organization
  fn: CCSD
keyword: keller-segel-model
keyword: equation-de-vlasov-poisson
keyword: asymptotiques-en-temps-grand
keyword: equilibre-relatif
keyword: matched-asymptotics-expansion
keyword: lyapunov-functional
keyword: n-body-problem
keyword: solutions-auto-similaires
keyword: large-time-asymptotics
keyword: energie-libre
keyword: continous-stellar-dynamics
keyword: trou-spectral
keyword: free-energy
keyword: subcritical-mass
keyword: reduction-de-lyapunov-schmidt
keyword: entropie-relative
keyword: relative-entropy
keyword: logarithmic-hardy-littlewood-sobolev-inequality
keyword: lyapunov-schmidt-reduction
keyword: chemotaxis
keyword: masse-critique
keyword: exposant-critique
keyword: spectral-gap
keyword: theses
keyword: developpement-asymptotique
keyword: relative-equilibrium
keyword: fonctionnelle-de-lyapunov
keyword: bubble-tower-solutions
keyword: modele-de-keller-segel
keyword: probleme-a-n-corps
keyword: vlasov-poisson-equation
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: self-similar-solutions
keyword: chemotactisme
keyword: inegalite-logarithmique-de-hardy-littlewood-sobolev
keyword: tour-de-bulles
keyword: critical-exponent
landing page: https://theses.hal.science/tel-00861568
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

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

test_moissonnage_selune
type: Agent