Exponentially sensitive internal layer solutions of one-side and their asymptotic expansions
- Bohé, Adriana
2010 Mathematics Subject Classification
- 34B15 34E15
- Internal layers, exponentially sensitive boundary value problems, Gevrey expansions
We consider a singularly perturbed boundary value problem with Dirichlet conditions and study the sensitivity of the internal layers solutions with respect to small changes in the boundary data. Our approach exploits the existence of smooth invariant manifolds and their asymptotic expansions in the small parameter of perturbation. We show that the phenomenon is extremely sensitive since the shock layers are only obtained by exponentially small perturbations of the boundary data.