科研之友
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摘要
In this paper we study a model of necrotic tumor growth. The tumor comprises necrotic cells which occupy a radially symmetric core and life proliferating cells which occupy a radially symmetric shell adjacent to the core. The proliferating cells receive nutrients through diffusion from the outer boundary as well as by means of blood now through a network of capillary vessels. The mathematical model describes the evolution of the nutrient concentration a between the boundary of the necrotic core r = rho (t) and the outer boundary of the tumor r = R(t); within the core itself the concentration is a constant a = a a level under which life nec, cells cannot be sustained. Both of the surfaces r = rho (t) and r = R(t) are free boundaries, which are unknown in advance. Under some assumptions on the parameters, we prove that (i) there exists a stationary solution with radii r = rho (s), r = R,; (ii) for any initial data near the stationary solution, the time dependent model has a unique solution sigma (r, t) with free boundaries r = rho (t), r = R(t); and (iii) rho (t) --> rho (s) and R(t) --> R-s as t --> infinity.
- 出版日期2001-3-15
- 单位中山大学
