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Diffusion modeling of tumor-CD4$ ^+ $-cytokine interactions with treatments: asymptotic behavior and stationary patterns

  • * Corresponding author: Wenbin Yang

    * Corresponding author: Wenbin Yang 

The first author is supported by NSF of China grant 12001425

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  • In this work, we consider a diffusive tumor-CD4$ ^+ $-cytokine interactions model with immunotherapy under homogeneous Neumann boundary conditions. We first investigate the large-time behavior of nonnegative equilibria, including the system persistence and the stability conditions. We also give the existence of nonconstant positive steady states (i.e., a stationary pattern), which indicate that this stationary pattern is driven by diffusion effects. For this study, we employ the comparison principle for parabolic systems, linearization method, the method of energy integral and the Leray-Schauder degree.

    Mathematics Subject Classification: Primary: 35B40, 35B36; Secondary: 35K57.


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