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Toyohiko Aiki
| Speaker: |
Prof. Toyohiko Aiki (Gifu, Japan)
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| Date: |
Thursday November 6, 2008
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| Title: |
A free
boundary problem for a SMA valve with the unknown temperature
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Abstract
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In this talk let us
consider a free boundary problem describing a change of the length of a
one-dimensional elastic material. By elementary calculation the free
boundary
problem is given as the initial boundary value problem for the
hyperbolic
equation with dynamic boundary condition. Moreover, as the practical
example
for the elastic material we deal with a new mathematical model for a
valve made
of a shape memory alloy spring and a normal spring. The model is given
by the
following initial boundary value problem:
where ρ1 (resp. ρ2)
is the density of the shape memory alloy (resp. the normal) spring, γ is a positive constant, θ is the temperature field, f : R → R is the free energy
function, g1, g2 and g3 are given functions,
and u01, v01, u02, v02 and q0 are initial functions. |
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