| Abstract: |
| We consider a system of strain-gradient viscoelasticity arising in phase transition models, with a particular focus on nonlinear dispersive effects. In the onedimensional case, we prove the existence of weak solutions under minimal assumptions, highlighting the role of nonlinear strain-gradient terms in the analysis. In the case of constant dispersion and in the multi-dimensional case, we prove global existence results and investigate the zero dispersion limit, including a rate of convergence in two space dimensions. We conclude by discussing some of the main challenges that arise in the presence of physical boundaries. |
|