Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.01183 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910184971960320 |
|---|---|
| author | Affouf, M. |
| author_facet | Affouf, M. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01183 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Smooth Solutions to a Thermoelastic Cauchy Problem in Phase Transitions Affouf, M. Analysis of PDEs 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. |
| title | Global Smooth Solutions to a Thermoelastic Cauchy Problem in Phase Transitions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.01183 |