3-维肿瘤模型解的非对称稳定性

The asymmetry stability of the solutions to a 3-dimensional tumor model

肿瘤的非对称不稳定性,通常暗含肿瘤会浸润周围正常组织.为了研究一个考虑了细胞黏附力的未血管化3-维肿瘤的非对称稳定性,首先对该肿瘤模型球对称静止解增加了非对称扰动,应用Taylor展开,考虑了非对称扰动的线性化问题,即一个关于扰动的偏微分方程初值问题.然后利用球调和函数展开,研究了有关扰动的偏微分方程的变量分离形式的解,最后根据微分方程稳定性定理,在肿瘤静止半径没有限制或肿瘤静止半径小于1的情况下,得到了非对称扰动的稳定和不稳定的条件.

The asymmetry instability of a tumor usually imply the tumor could infiltrate the surrounding normal tissue. To study the asymmetry stability of a 3-dimensional avascular tumor with adhesive forces, the symmetry stationary solutions to the model were added a asymmetry disturbance, by Taylor expansion, a linear model about the asymmetry disturbance, an initial value problem of partial differential equations, was studied. By the expansion of a function in terms of spherical harmonics, solutions in form of separation about the asymmetry disturbance were studied. At last, by the theory of stability of differential equations, under the no limitation or less than 1 to the symmetry stationary radius, the asymmetry stability of stable and unstable conditions were obtained.