TY - JOUR
T1 - Asymptotic stability of constant steady states for a 2 2 reaction-diffusion system arising in cancer modelling
AU - Di Francesco, M.
AU - Twarogowska, M.
PY - 2011/4/1
Y1 - 2011/4/1
N2 - The dependence of tumor on essential nutrients is known to be crucial for its evolution and has become one of the targets for medical therapies. Based on this fact a reaction-diffusion system with chemotaxis term and nutrient-based growth of tumors is presented. The formulation of the model considers also an influence of tumor and pharmacological factors on nutrient concentration. In the paper, convergence of solutions to constant, stationary states in the one-dimensional case for small perturbation of the equilibria is investigated. The nonlinear stability results are obtained by means of the classical symmetrization method and energy Sobolev estimates.
AB - The dependence of tumor on essential nutrients is known to be crucial for its evolution and has become one of the targets for medical therapies. Based on this fact a reaction-diffusion system with chemotaxis term and nutrient-based growth of tumors is presented. The formulation of the model considers also an influence of tumor and pharmacological factors on nutrient concentration. In the paper, convergence of solutions to constant, stationary states in the one-dimensional case for small perturbation of the equilibria is investigated. The nonlinear stability results are obtained by means of the classical symmetrization method and energy Sobolev estimates.
UR - http://www.scopus.com/inward/record.url?scp=79951575832&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1016/j.mcm.2010.03.034
U2 - 10.1016/j.mcm.2010.03.034
DO - 10.1016/j.mcm.2010.03.034
M3 - Article
AN - SCOPUS:79951575832
SN - 0895-7177
VL - 53
SP - 1457
EP - 1468
JO - Mathematical and Computer Modelling
JF - Mathematical and Computer Modelling
IS - 7-8
ER -