Adomian分解法求解含非线性源的Burgess方程
Applying Adomian Decomposition Method to Solve Burgess Equation with a Non-linear Source
摘要：
在目前的工作中，我们考虑的数学模型，描述了脑肿瘤的生长（胶质母细胞瘤）下的医疗。基于R. Stupp等人（New Engl Journal of Med 352：987 - 996，2005）证明了联合疗法如放疗和化疗产生负肿瘤生长，并使用P.K. Burgess等人（J Neuropath and Exp Neur 56：704 - 713，1997）作为起点，我们提出了一个在药物治疗下的肿瘤生长模型，该模型由使用Adomian分解方法（ADM）求解的非线性偏微分方程表示。它还表明，非线性项有效地模拟联合治疗的效果。通过合理地使用参数，该模型可用于放疗和化疗的剂量计算。
英文摘要：
In the present work we consider the mathematical model that describes brain tumour growth (glioblastomas) under medical treatment. Based on the medical study presented by R. Stupp et al. (New Engl Journal of Med 352: 987-996, 2005) which evidence that, combined therapies such as, radiotherapy and chemotherapy, produces negative tumour-growth, and using the mathematical model of P. K. Burgess et al. (J Neuropath and Exp Neur 56: 704-713, 1997) as an starting point, we present a model for tumour growth under medical treatment represented by a non-linear partial differential equation that is solved using the Adomian Decomposition Method (ADM). It is also shown that the non-linear term efficiently models the effects of the combined therapies. By means of a proper use of parameters, this model could be used for calculating doses in radiotherapy and chemotherapy.
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