| Name |
Michael Herrmann |
| Country |
Germany |
| Email |
michael.herrmann@math.uni-sb.de |
| Co-Author(s) |
Karsten Matthies, Hartmut Schwetlick, Johannes Zimmer |
| Submit Time |
2014-02-28 08:40:07 |
Session |
Special Session 101: Nonlinear waves in materials with microstructure
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| Contents |
| Traveling waves in atomic chains with non convex potential energy play an important
role in physics and materials science since they provide the kinetic relation for more
complex phenomenological models. Unfortunately, very little is known about such waves
and most of the available results are restricted to piecewise affine nonlinearities. In this
talk we consider genuinely nonlinear perturbations of a bi-quadratic double-well potential
and show that the corresponding three-parameter family of phase-transition waves persists
provided that the perturbation is sufficiently small and localized with respect to the strain
variable. Our perturbative methods is nonlocal and nonlinear but does not alter the
asymptotic oscillations in front of the interface. As a consequence we can identify a unique
one-parameter sub-family of waves satisfying the causality principle. |
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