In order to understand the effects of cellular diffusion on the dynamic behaviors of cancer cell subpopulations,we establish a reaction-diffusion model of the competition between drug-sensitive and drug-resistant canc...In order to understand the effects of cellular diffusion on the dynamic behaviors of cancer cell subpopulations,we establish a reaction-diffusion model of the competition between drug-sensitive and drug-resistant cancer cells.Firstly,taking drug dosage and diffusion coefficients as bifurcation parameters,we investigate the Turing instability conditions for the drug-sensitive and drug-resistant cancer cell model driven by passive-diffusion and cross-diffusion factors at the positive steady state solution,and obtain the distribution regions of the model undergoing Turing instability.Secondly,we deduce the wave speed conditions for the three types of traveling wave solutions connecting two nontrivial steady state solutions,and prove the existence of traveling wave solutions driven by passive-diffusion,using the eigenvalue analysis method,the upper and lower solution method,and Schauder’s fixed point theorem.Finally,we perform some numerical simulations to verify the results of the obtained theories and give the spatially inhomogeneous steady state solutions and the traveling wave solutions,as well as the wave solutions of the non-uniformity diffusion with different temporal and spatial locations.展开更多
文摘In order to understand the effects of cellular diffusion on the dynamic behaviors of cancer cell subpopulations,we establish a reaction-diffusion model of the competition between drug-sensitive and drug-resistant cancer cells.Firstly,taking drug dosage and diffusion coefficients as bifurcation parameters,we investigate the Turing instability conditions for the drug-sensitive and drug-resistant cancer cell model driven by passive-diffusion and cross-diffusion factors at the positive steady state solution,and obtain the distribution regions of the model undergoing Turing instability.Secondly,we deduce the wave speed conditions for the three types of traveling wave solutions connecting two nontrivial steady state solutions,and prove the existence of traveling wave solutions driven by passive-diffusion,using the eigenvalue analysis method,the upper and lower solution method,and Schauder’s fixed point theorem.Finally,we perform some numerical simulations to verify the results of the obtained theories and give the spatially inhomogeneous steady state solutions and the traveling wave solutions,as well as the wave solutions of the non-uniformity diffusion with different temporal and spatial locations.
