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PreprintCC BY 4.0arXiv

On the unconstrained Allen-Cahn system and its Cahn-Hilliard limit

  • P. O. Mchedlov-Petrosyan
  • L. N. Davydov
  • O. A. Osmayev
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Abstract

In [F.P. Duda et al., Meccanica, 2021] the new theory for constituent migration in solids with microstructure was developed. We consider the one-dimensional version of the basic system of this theory with generally non-zero kinetic modulus and the particular diffusivity of the "fast diffusion" type. We obtain exact traveling wave solutions for this system, and analyze several unconstraint and constraint limiting cases. We show that in unconstraint cases of Allen-Cahn type, i.e. for two independent variables, the system demonstrates broader set of possible regimes; in the constraint limit only CH-type process remains.

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Cite

BibTeXRIS
BibTeX
@misc{mchedlovpetrosyan2026unconstrained,
  title = {{On the unconstrained Allen-Cahn system and its Cahn-Hilliard limit}},
  author = {P. O. Mchedlov-Petrosyan and L. N. Davydov and O. A. Osmayev},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00778},
  eprint = {2611.00778},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00778},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the unconstrained Allen-Cahn system and its Cahn-Hilliard limit
AU  - P. O. Mchedlov-Petrosyan
AU  - L. N. Davydov
AU  - O. A. Osmayev
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00778
UR  - https://arxiv.org/abs/2611.00778
AB  - In [F.P. Duda et al., Meccanica, 2021] the new theory for constituent migration in solids with microstructure was developed. We consider the one-dimensional version of the basic system of this theory with generally non-zero kinetic modulus and the particular diffusivity of the "fast diffusion" type. We obtain exact traveling wave solutions for this system, and analyze several unconstraint and constraint limiting cases. We show that in unconstraint cases of Allen-Cahn type, i.e. for two independent variables, the system demonstrates broader set of possible regimes; in the constraint limit only CH-type process remains.
ER  -