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We consider a system of two hyperbolic equations for p, q and two elliptic equations for c, , where p, q are the densities of cells within the tumor ₜ in proliferating and quiescent states, respectively, c is the concentration of nutrients, and is the pressure. The pressure is a result of the transport of cells which proliferate or die. The motion of the free boundary ₜ is given by the continuity condition, and at the free boundary is proportional to the surface tension. We prove the existence, uniqueness, and regularity of the solution for a small time interval 0 t T.
Chen et al. (Wed,) studied this question.
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