Large time behaviour of a diffusion equation with strong convection
Dans cette article, on étudie la limite lorsque m --> ∞ de la solution du problème de Cauchy ut - ∆um + div F(u) = 0 sur un ouvert Omega avec des conditions aux bords de type Dirichlet et une donnée initiale u0 ≥ 0.
We study one-dimensional linear hyperbolic systems with -coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of solutions in the whole scale of Sobolev-type spaces of periodic functions. These spaces give an optimal regularity trade-off for our problem.
This paper is divided into two parts and focuses on the linear independence of boundary traces of eigenfunctions of boundary value problems. Part I deals with second-order elliptic operators, and Part II with Stokes (and Oseen) operators. Part I: Let be an eigenvalue of a second-order elliptic operator defined on an open, sufficiently smooth, bounded domain Ω in ℝⁿ, with Neumann homogeneous boundary conditions on Γ = tial Ω. Let be the corresponding linearly independent (normalized) eigenfunctions...