## On a Barodiffusion Problem in Region with Moving Boundary

J. Math. Sci. Univ. Tokyo
Vol. 4 (1997), No. 1, Page 1--31.

Åukaszewicz, Grzegorz
On a Barodiffusion Problem in Region with Moving Boundary
Consider isothermic flow of a mixture of two viscous fluids with densities $Ï_1$ and $Ï_2$, and velocities $u_1$ and $u_2$, respectively, with $Ï_1 + Ï_2 = constant >0$. The diffusion effect then is associated only with changes of pressure and concentrations of the components of the mixture. The flow can be described by a closed system of equations involving mean mass velocity vector $u$, pressure $p$, and concentration of one of its components $c$. We assume that at each time $t$, $0\leq t\leq T$, $T> 0$, the mixture occupies a given bounded region $Î©_t$ in $R^3$, and prove two existence theorems (local and global one) for an initial boundary value problem for the system of equations governing its flow: \roster \item"(1)" For an arbitrary data the considered problem has a solution $(u,p,c)$ in some domain $Q_{T^{\ast}}=\bigcup_{00$, \$0