  In the Ginzburg-Landau equation, there are domain walls connecting two
metastable states. The dynamics of domain walls has been intensively studied,
but there remain still unsolved but crucial problems even for a single domain.
We study the domain wall dynamics in three different Ginzburg-Landau-type
equations satisfying conservation laws. In a modified $\phi^4$ model satisfying
the law of energy conservation and the Lorentz invariance, the motion of a
domain wall is accelerated and the velocity approaches its maximum. In a
one-dimensional model of eutectic growth, the order parameter is conserved and
a domain wall connecting a metastable uniform state and a spatially periodic
pattern appears. We try to find a selection rule for the wavelength of a
spatially periodic pattern. In a model equation for martensitic transformation,
a domain wall connecting a uniform metastable state and a zigzag structure
appears which propagates at a high velocity.
