A hyperbolic free boundary problem modeling tumor growth: Asymptotic behavior

作者：Chen, XF^*; Cui, SB; Friedman, A

来源：Transactions of the American Mathematical Society, 2005, 357(12): 4771-4804.

DOI：10.1090/S0002-9947-05-03784-0

• tumor growth
• free boundary problem
• stationary solution
• asymptotic behavior

In this paper we study a free boundary problem modeling the growth of radially symmetric tumors with two populations of cells: proliferating cells and quiescent cells. The densities of these cells satisfy a system of nonlinear first order hyperbolic equations in the tumor, and the tumor's surface is a free boundary r = R(t). The nutrient concentration satisfies a diffusion equation, and R( t) satisfies an integro-differential equation. It is known that this problem has a unique stationary solution with R( t) = R-s. We prove that ( i) if lim(T-->infinity) integral(T 1)(T)\(r) over dot(t)\dt = 0, then lim(t-->infinity)R(t) = R-s, and ( ii) the stationary solution is linearly asymptotically stable.

• 出版日期2005
• 单位中山大学