Um problema de fronteira livre para um sistema eliptico-hiperbolico : uma aplicação ao crescimento de tumores / A free boundary problem for an elliptic-hyperbolic system : an application to tumor growth

AUTOR(ES)
DATA DE PUBLICAÇÃO

2010

RESUMO

In this dissertation we detail the analysis done in the article by X. Chen, A. Friedman, A free boundary problem for an elliptic-hyperbolic system,: an application to tumor growth, SIAM J. Math. Anal. 35, 2003, which considers a free boundary value problem for an elliptic-hyperbolic system of partial differential equations related to the Hele-Shaw problem. The present problem models the growth of a tumor and takes in consideration the following possibilities for the state of a tumor cell: proliferating, quiescent or necrotic; the model also takes in consideration the available nutrient concentration. The equations hold in a time varying domain in such way that the boundary velocity depends on the other variables of the problem. As a result of the analysis, we obtain the local in time existence, as well as uniqueness, of classical solutions for the system

ASSUNTO(S)

free boundary problem elliptic differential equations tumor growth hyperbolic differential equations equações diferenciais elipticas problema de fronteira livre equações diferenciais hiperbolicas tumores - crescimento

ACESSO AO ARTIGO

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