Abstract
This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary Γ : y = g(x, t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.
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