We study the multi-phase Stefan problem with increasing Riemann initial data and generally negative latent specific heats for phase transitions. We propose a variational formulation of self-similar solutions, which allows us to find precise conditions for the existence and uniqueness of a solution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural’tseva, Linear and Quasi-Linear Equations of Parabolic Type, Am. Math. Soc., Providence, RI (1968).
V. V. Pukhnachev, “Occurrence of a singularity in the solution of a Stefan-type problem” Differ. Equations 16, 313–318 (1980).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Panov, E.Y. Solutions of An Ill-Posed Stefan Problem. J Math Sci 274, 534–543 (2023). https://doi.org/10.1007/s10958-023-06618-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06618-4