-preserving Schrödinger heat flow under the Ricci flow.
-estimates for solutions of Dirichlet and Neumann problems to heat equation in the wedge with edge of arbitrary codimension
La diffusione del calore in uno strato di spessore variabile in presenza di scambi termici non lineari con l'ambiente. (I) Deduzione di limitazioni a priori sulla temperatura e le sue derivate
Laplace transform representations and Paley-Wiener theorems for functions on vertical strips.
Large time behaviour of heat kernels on non-compact manifolds: fast and slow decays
In this talk we shall present some joint work with A. Grigory’an. Upper and lower estimates on the rate of decay of the heat kernel on a complete non-compact riemannian manifold have recently been obtained in terms of the geometry at infinity of the manifold, more precisely in terms of a kind of isoperimetric profile. The main point is to connect the decay of the norm of the heat semigroup with some adapted Nash or Faber-Krahn inequalities, which is done by functional analytic methods. We shall...
Large time behaviour of solutions of the heat equation with absorption
Large time behaviour of the solutions to some nonlinear evolution equations
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.