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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.01183 |
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Table of Contents:
- We study one-dimensional viscoelastic phase transitions modeled by a Ginzburg--Landau energy with a non-convex cubic stress-strain law. Extending the isothermal model, we couple the momentum equation to a heat equation for the temperature field, giving a thermoelastic system with viscous, capillary, and thermal-diffusion terms. We prove global existence and uniqueness of classical smooth solutions for the Cauchy problem, using a traveling-wave decomposition, an exponential transformation of the mechanical perturbation, and coupled energy estimates at successive regularity levels. Under additional integrability and small-data assumptions, the temperature perturbation decays algebraically.