Singular limit of an integrodifferential system related to the entropy balance

TL;DR

This paper investigates the singular limit of an integrodifferential PDE system modeling phase transitions with thermal memory, providing convergence results and error estimates as the memory kernel approaches a delta distribution.

Contribution

It introduces a rigorous analysis of the singular limit in a thermodynamic model with thermal memory, including convergence and error estimates for the PDE system.

Findings

Convergence of the integrodifferential system to a local PDE as the memory kernel becomes singular.

Error estimates quantifying the approximation accuracy in the singular limit.

Validation of the model's consistency with classical phase transition equations.

Abstract

A thermodynamic model describing phase transitions with thermal memory, in terms of an entropy equation and a momentum balance for the microforces, is adressed. Convergence results and error estimates are proved for the related integrodifferential system of PDE as the sequence of memory kernels converges to a multiple of a Dirac delta, in a suitable sense.