On some elliptic problems ok Kirchhoff-type and fluid dynamics
type: Dataset
description: This thesis consists of two independent parts. The first is devoted to the study of some elliptic problems of Kirchhoff-type in the following form : -M(ʃΩNul² dx) Δu = f(x, u) xЄΩ ; u(x) = o xЄƋΩ where Ω cRN, N ≥ 2, f is a Caratheodory function and M is a strictly positive and continuous function on R+. In the case where the function f is asymptotically linear at infinity with respect to the unknown u, we show, by combining a truncation technique and the variational method, that the problem admits a positive solution when the function M is nondecreasing. And if f(x, u) = |u|p-1 u + λg(x) where p> 0, λ a real parameter and g is a function of class C1 and changes the sign in Ω, then under some assumptions on M, there exist two positive real λ. and λ. such that the problem admits positive solutions if 0 < λ <λ., and no positive solutions if λ > λ.. In the second part, we study two problems arising in fluid dynamics. The first is a generalization of a model describing the unidirectional propagation of long waves in dispersive medium with two fluids. By writing the problem as a fixed point equation, we prove the existence of at least one positive solution. We then show its symmetry and uniqueness. The second problem is to prove the existence of the velocity, pressure and temperature of a non-Newtonian, incompressible and isothermal fluid, occupying a bounded domain, taking into account a convection term. The originality in this work is that the fluid viscosity depends not only on the velocity but also on the temperature and the modulus of deformation rate tensor. Based on the notion of pseudo-monotone operators, the De Rham theorem and the Schauder fixed point theorem, the existence of the triplet, (velocity, pressure, temperature) is shown
identifier: NNT: 2012STET4016
issued: 2026-05-05T17:46:02.471774
language: fr
modified: 2026-05-05T17:46:02.471778
contact point: Organization
  fn: CCSD
keyword: approche-de-galerkin
keyword: de-rham-theorem
keyword: equation-de-type-de-kirchhoff
keyword: fluide-non-newtonien
keyword: fonction-de-green
keyword: galerkin-methods
keyword: greens-functions
keyword: infoeu-reposemanticsdoctoralthesis
keyword: kirchhoff-equation-type
keyword: loi-de-tresca
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: methode-de-sous-et-sur-solutions
keyword: methode-variationnelle
keyword: non-newtonian-fluid
keyword: theoreme-de-de-rham
keyword: theses
keyword: trescas-law
keyword: variational-method
landing page: https://theses.hal.science/tel-00971279

On some elliptic problems ok Kirchhoff-type and fluid dynamics
type: Distribution
format: HTML
issued: 2026-05-05T17:46:02.480706
modified: 2026-05-05T17:46:02.450769
access URL: https://theses.hal.science/tel-00971279

test_moissonnage_selune
type: Agent