Project R-9130

Approximations for forward and inverse reaction-diffusion problems related to cancer models. (Research)

Nowadays, cancer is well known to be one of the most life-threatening diseases in the world. The incidence of cancer among people has drastically been increasing year by year. Until now, the major impediment for scientists is finding the leading cause as well as understanding the whole complex mechanisms of this disease to eventually figure out a therapeutical treatment. Mathematical modeling for cancer cell populations is commonly used to get an insight into cancer growth and invasion. The so-called mathematical oncology aims at using mathematical and computational methods to explain related issues and concepts of cancer and for their potential treatments. It is not only helpful in analyzing the behaviors of cancer cells, but also further constructive in predicting the progression of neoplasms. It is worth noting that cancer is an age-related disease that causes the outgrowth of cell populations in a specific part of the human body. This cause, concurrent with principally misdirecting T cells of the immune system, makes cancer mostly untreatable and thus becomes the general cause of death in cancer patients. As part of population dynamics, the age dependence also leads to the morbidity and mortality of the involved cell population. In this project, we will develop approximation methods for some forward and inverse reaction-diffusion problems related to cancer models, which have not been solved yet. Moreover, convergence analysis will be carried out.

01 October 2018 - 16 February 2021