| Contents |
| We analyse the travelling wave problem
for a lattice model of elastic phase transitions. In particular we consider a bistable model
with a piecewise quadratic interaction potential and a smoothed variant with small spinodal
region. A number of authors have been able to prove in both cases the existence of families of
subsonic travelling waves, so that special interest is focusing on relevant selection
criteria to identify meaningful solutions.
Following ideas from vanishing viscosity approach to conservation laws
we present ideas to analyse the stabilisation of waves in the model with dissipation and
discuss how this might help to set up a framework for the interpretation of the various types of wave solutions existing for the FPU lattice problem.
This is joint work with M Herrmann (Saarbruecken), K Matthies, J Zimmer (Bath). |
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