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We consider a system of two hyperbolic equations for p,q and two elliptic equations for c,σ, where p,q are the densities of cells within the tumor Ωₜ in proliferating and quiescent states, respectively, c is the concentration of nutrients, and σ is the pressure. The pressure is a result of the transport of cells which proliferate or die. The motion of the free boundary ∂ Ωₜ is given by the continuity condition, and σ 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.
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Chen et al. (2003) studied this question.
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