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The existence and uniqueness of global solutions to a mathematical model for shape memory alloys. (English) Zbl 0841.73032
Summary: This paper deals with the well-posedness of a mathematical model for the vibration of a thin wire composed of a shape memory alloy. The existence and uniqueness of global solutions in both cases of Neumann and Dirichlet boundary conditions for the absolute temperature \(\theta\) are investigted.

MSC:
74H45 Vibrations in dynamical problems in solid mechanics
74A15 Thermodynamics in solid mechanics
80A22 Stefan problems, phase changes, etc.
35Q72 Other PDE from mechanics (MSC2000)
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