A free boundary problem for an elliptic-hyperbolic system: an application to tumor growth

• Grant number: 07/06070-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2008
• End date: February 28, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Jose Luiz Boldrini
• Grantee: Meire Fortunato
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 04/07075-7 - Immune-epidemiology of infectious diseases: quantitative approaches considering clinical, therapeutic and prophylactic aspects, AP.TEM

Abstract

In this project we will analyze in a mathematically rigorous way a free boundary value problem consisting of a elliptic-hyperbolic system of partial differential equations related to the Hele-Shaw problem. The problem in the project models the growth of a tumor and takes in consideration the following possibilities for the state of a tumor cell: proliferating cells, quiescent cells or necrotic cells; the model also take in consideration the nutrient concentration in the tumor. The equations hold in a time varying domain depending on the other variables of the problem. The main objective of the project is a local in time existence of solutions for the system, as well as their uniqueness.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

FORTUNATO, Meire. A free boundary problem for an elliptic-hyperbolic system: an application to tumor growth. 2010. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.