Diffusion effects on a superconductive model

Abstract

A superconductive model characterized by a third order parabolic operator L" is analysed. When the viscous terms, represented by higher - order deriva- tives, tend to zero, a hyperbolic operator L0 appears. Furthermore, if P" is the Dirichlet initial boundary - value problem for L", when L" turns into L0; P" turns into a problem P0 with the same initial - boundary conditions as P". The solution of the nonlinear problem related to the remainder term r is achieved, as long as the higher-order derivatives of the solution of P0 are bounded. More- over, some classes of explicit solutions related to P0 are determined, proving the existence of at least one motion whose derivatives are bounded. The estimate shows that the diffusion effects are bounded even when time tends to infinity.