Traveling waves in rapid solidification

Karl Glasne, Karl B Glasner

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We analyze rigorously the one-dimensional traveling wave problem for a thermodynamically consistent phase field model. Existence is proved for two new cases: one where the undercooling is large but not in the hypercooled regime, and the other for waves which leave behind an unstable state. The qualitative structure of the wave is studied, and under certain restrictions monotonicity of front profiles can be obtained. Further results, such as a bound on propagation velocity and non-existence are discussed. Finally, some numerical examples of monotone and non-monotone waves are provided.

Original languageEnglish (US)
JournalElectronic Journal of Differential Equations
Volume2000
StatePublished - 2000
Externally publishedYes

Fingerprint

Solidification
Traveling Wave
Phase Field Model
Nonexistence
Monotonicity
Monotone
Unstable
Propagation
Restriction
Numerical Examples

Keywords

  • Phase field models
  • Traveling waves

ASJC Scopus subject areas

  • Analysis

Cite this

Traveling waves in rapid solidification. / Glasne, Karl; Glasner, Karl B.

In: Electronic Journal of Differential Equations, Vol. 2000, 2000.

Research output: Contribution to journalArticle

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