Global existence for a strongly coupled Cahn-Hilliard system with viscosity (Q2869747)

An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions, NEWLINE\[NEWLINE (1+2g(\rho))\partial_t\mu+\mu g\prime (\rho)\partial_t \rho-\text{ div} (k(\mu,\rho)\nabla \mu)=0, NEWLINE\]NEWLINE NEWLINE\[NEWLINE \partial_t \rho-\Delta\rho+f\prime(\rho)=\mu g\prime (\rho), NEWLINE\]NEWLINE NEWLINE\[NEWLINE (k(\mu,\rho)\nabla\mu)\cdot\nu|_{\Gamma}=0,\qquad\text{and}\qquad \partial_\nu\rho|_\Gamma=0, NEWLINE\]NEWLINE NEWLINE\[NEWLINE \mu(0)=\mu_0 ,\qquad\text{and}\qquad \rho(0)=\rho_0. NEWLINE\]