We analyze the growth of a droplet of a stable phase (a plane wave front in
one-dimensional case) under strong supercooling in the framework of the La
ndau-Ginzburg potential for both a conserved and a nonconserved order param
eter coupled to thermal diffusion. When the coupling between changes in tem
perature and the order parameter is strong enough, and the heat conductivit
y is sufficiently small, the following nontrivial phenomenon may occur: the
latent heat released with the growth of a droplet is taken away very slowl
y, and the local overheating transforms the initially overcooled state into
an overheated one. As a result, the rate of droplet growth decreases, and
even may change its sign, so that droplets of radius larger than the critic
al one, nevertheless, may shrink. For the steady-state growth in the one-di
mensional case this phenomenon was analyzed analytically, while beyond the
steady regime and in the two-dimensional case, the equations were solved nu
merically. The presence of a thermal bath with heat loss through thermal di
ssipation narrows the areas of occurence of this phenomenon. (C) 2000 Ameri
can Institute of Physics. [S0021-9606(00)50742-9].