Abstract
We study a quasilinear partial differential equation which is a classical unidimensional model of fluid motion (Burgers equation). We consider the problem in a finite interval with stationary boundary conditions. The aim is to see whether the model shows transitions in the asymptotic behaviour as viscosity varies. We show that there is always a unique stationary solution, which is explicitely exhibited, and, by using the Hopf-Cole transformation, that it is globally attractive for any value of the viscosity, both in the homogeneous and inhomogeneous case.
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