Weak solutions to the phase field system

V. G. Danilov*, G. A. Omel'yanov, E. V. Radkevich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We consider a new concept of weak solutions to the phase field equations with a small parameter ε characterizing the length of interaction. For the standard situation of a single free interface, this concept (in contrast to the common one) leads to the well-known Stefan-Gibbs-Thomson problem as ε → 0. For the case of a large number M(ε) (M(ε) → ∞ as ε → 0) of free interfaces, which is related to the "wave-train" interpretation of a "mushy region", this concept allows us to obtain limiting problems as ε → 0.

Original languageEnglish
Pages (from-to)27-35
Number of pages9
JournalIntegral Transforms and Special Functions
Issue number1-4
StatePublished - 1998
Externally publishedYes

Bibliographical note

Funding Information:
If = 1 for x E R \ R: and F ( x ) 5 const < 0 for + E E, then the domain R: transforms to the domain R, of "solid" in which = -1. This work was partially supported by the Russian Foundation for Basic Research, grant N 96-01-01492.


  • Limiting problem
  • Mushy region
  • Wave-train
  • Weak solution


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