| Abstract: |
| This talk presents an extension of a previously studied class of chemotaxis systems, in which a source term of logistic type is introduced into one of the three parabolic partial differential equations. The source term of logistic type is given by the expression $u^k(1-u)$. This choice generalizes some models previously described in literature. We study some properties of the classical solutions for the superquadratic and quadratic degradation rate, i.e., $k>1$ and $k=1$ respectively. Under suitable assumptions on the initial data and the coefficients of the system, the global-in-time existence of the classical solutions and their uniform boundedness are proved in bounded domains of $\mathbb{R}^n$, $n \geq 3$. |
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