Global Smooth Solutions to a Thermoelastic Cauchy Problem in Phase Transitions

M. Affouf

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arXiv · 2605.01183

Global Smooth Solutions to a Thermoelastic Cauchy Problem in Phase Transitions

M. Affouf

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Abstract

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.

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M. Affouf. 2026-05-02. Global Smooth Solutions to a Thermoelastic Cauchy Problem in Phase Transitions. https://arxiv.org/abs/2605.01183

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