On homogenization of a diffusion perturbed by a periodic reflection invariant vector field.
Viene dimostrata l'esistenza di soluzioni del problema di Darboux per l'equazione iperbolica sul planiquarto , . Qui, è una funzione continua, con valori in uno spazio Banach che soddisfano alcune condizioni di regolarità espresse in termini della misura di non-compattezza .
The paper deals with the problem of finding a curve, going through the interior of the domain , accross which the flux , where is the solution of a mixed elliptic boundary value problem solved in , attains its maximum.
We study a family of semilinear reaction-diffusion equations on spatial domains , ε > 0, in lying close to a k-dimensional submanifold ℳ of . As ε → 0⁺, the domains collapse onto (a subset of) ℳ. As proved in [15], the above family has a limit equation, which is an abstract semilinear parabolic equation defined on a certain limit phase space denoted by . The definition of , given in the above paper, is very abstract. One of the objectives of this paper is to give more manageable characterizations...