Hugoniot-type conditions and weak solutions to
the phase-field system
1999 ◽
Vol 10
(1)
◽
pp. 55-77
◽
Keyword(s):
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 with 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 corresponds to the ‘wave-train’ interpretation of a ‘mushy region’, this concept allows us to obtain the limit problem as ε→0.
2017 ◽
Vol 74
(7)
◽
pp. 1542-1564
◽
2017 ◽
Vol 77
(4)
◽
pp. 1471-1492
◽
Keyword(s):
2020 ◽
Vol 36
(3)
◽
pp. 235-242
◽
2011 ◽
Vol 24
(4-6)
◽
pp. 437-459
◽
Keyword(s):
Keyword(s):
Keyword(s):