We consider the asymptotic limit of a diffuse interface model fortumor-growth when a parameter $arepsilon$ proportional to the thickness ofthe diffuse interface goes to zero. An approximate solution which showsexplicitly the behavior of the true solution for small $arepsilon$ will beconstructed by using matched expansion method. Based on the energy method, aspectral condition in particular, we establish a smallness estimate of thedifference between the approximate solution and the true solution.
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