INTERNAL LAYERS, SMALL EIGENVALUES, AND THE SENSITIVITY OF METASTABLEMOTION

On a semi-infinite domain, an analytical characterization of exponenti ally slow internal layer motion for the Allen-Cahn equation and for a singularly perturbed viscous shock problem is given. The results exten d some previous results that were restricted to a finite geometry. For these slow motion problems, we show that the slow dynamics associated with the semi-infinite domain are not preserved, even qualitatively, by imposing a commonly used form of artificial boundary condition to t runcate the semi-infinite domain to a finite domain. This extreme sens itivity to boundary conditions and domain truncation is a direct resul t of the exponential ill-conditioning of the underlying linearized pro blem, For Burgers equation, many of the analytical results are verifie d by calculating certain explicit solutions. Some related ill-conditio ned internal layer problems are examined.