L'équation de la chaleur en plusieurs variables complexes
L...-Error Estimate for an Approximation of a Parabolic Variational Inequality.
Local exact controllability of the age-dependent population dynamics with diffusion.
Long time estimate of solutions to 3d Navier-Stokes equations coupled with heat convection
We examine the Navier-Stokes equations with homogeneous slip boundary conditions coupled with the heat equation with homogeneous Neumann conditions in a bounded domain in ℝ³. The domain is a cylinder along the x₃ axis. The aim of this paper is to show long time estimates without assuming smallness of the initial velocity, the initial temperature and the external force. To prove the estimate we need however smallness of the L₂ norms of the x₃-derivatives of these three quantities.
Long time existence of regular solutions to 3d Navier-Stokes equations coupled with heat convection
We prove long time existence of regular solutions to the Navier-Stokes equations coupled with the heat equation. We consider the system in a non-axially symmetric cylinder, with the slip boundary conditions for the Navier-Stokes equations, and the Neumann condition for the heat equation. The long time existence is possible because the derivatives, with respect to the variable along the axis of the cylinder, of the initial velocity, initial temperature and external force are assumed to be sufficiently...
Long-time dynamics of an integro-differential equation describing the evolution of a spherical flame.
This article is devoted to the study of a flame ball model, derived by G. Joulin, which satisfies a singular integro-differential equation. We prove that, when radiative heat losses are too important, the flame always quenches; when heat losses are smaller, it stabilizes or quenches, depending on an energy input parameter. We also examine the asymptotics of the radius for these different regimes.
Maximal function estimates for the parabolic mean value kernel.
Mean curvature and the heat equation.
Mean value densities for temperatures
A positive measurable function K on a domain D in is called a mean value density for temperatures if for all temperatures u on D̅. We construct such a density for some domains. The existence of a bounded density and a density which is bounded away from zero on D is also discussed.
Mémoire sur l'intégration des équations aux différences partielles de la Physique mathématique.
Monotonicity in time and stationary solutions for a quasilinear heat equation with source.
Nevanlinna's first fundamental theorem for supertemperatures.
New results on the Burgers and the linear heat equations in unbounded domains.
We consider the Burgers equation and prove a property which seems to have been unobserved until now: there is no limitation on the growth of the nonnegative initial datum u0(x) at infinity when the problem is formulated on unbounded intervals, as, e.g. (0 +∞), and the solution is unique without prescribing its behaviour at infinity. We also consider the associate stationary problem. Finally, some applications to the linear heat equation with boundary conditions of Robin type are also given.
Non linear schemes for the heat equation in 1D
Inspired by the growing use of non linear discretization techniques for the linear diffusion equation in industrial codes, we construct and analyze various explicit non linear finite volume schemes for the heat equation in dimension one. These schemes are inspired by the Le Potier’s trick [C. R. Acad. Sci. Paris, Ser. I 348 (2010) 691–695]. They preserve the maximum principle and admit a finite volume formulation. We provide a original functional setting for the analysis of convergence of such methods....
Nonexistence of global solutions to some differential inequalities of the second order and applications.
(Nonsymmetric) Dirichlet operators on : existence, uniqueness and associated Markov processes
Nonuniqueness for the heat flow of harmonic maps
Note on steady flow of heat in a semi-infinite strip
The existence of a solution of the two - dimensional heat conduction equation in a semi-infinite strip, under mixed boundary condition, is discussed.
Note to periodic solvability of the boundary value problem for nonlinear heat equation
Noyau de diffusion sur les espaces homogènes compacts