A kind of strongly coupled cross diffusion parabolic system, which can be used as the energy transport model in semiconductor science, is studied in this paper. The existence and uniqueness of strong soltution to the initial boundary value problem are obtained, under the condition that the initial data are a small perturbation of an isothermal stationary soltuion. Based on this result, an application of Newton iteration on solving this problem is also given.
"Strong Solutions to a Kind of Cross Diffusion Parabolic System." Commun. Math. Sci. 1 (4) 799 - 808, December 2003.