Stationary solutions to the Falk system on shape memory alloys

Takashi Suzuki, Souhei Tasaki

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We study the Falk model system describing martensitic phase transitions in shape memory alloys. Its physically closed stationary state is formulated as a nonlinear eigenvalue problem with a non-local term. Then, some results on existence, stability, and bifurcation of the solution are proven. In particular, we prove the existence of dynamically stable nontrivial stationary solutions.

Original languageEnglish
Pages (from-to)994-1011
Number of pages18
JournalMathematical Methods in the Applied Sciences
Volume33
Issue number8
DOIs
Publication statusPublished - 2010 May 30

Keywords

  • Falk model
  • Non-local elliptic problem
  • Shape memory
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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