  We study the domain growth of the one-dimensional kinetic Ising model under
the competing influence of Glauber dynamics at temperature T and Kawasaki
dynamics with a configuration-independent rate. The scaling of the structure
factor is shown to have the form for nonconserved dynamics with the corrections
arising from the spin-exchange process, i.e., $S(k,t)=Lg_0(kL,t/\tau
)+g_1(kL,t/\tau)+... $, and the corresponding scaling functions are calculated
analytically. A correction to the Porod law at zero temperature is also given.
