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On the global generalized solvability of a chemotaxis model with signal absorption and logistic growth terms (1805.09205v1)

Published 23 May 2018 in math.AP

Abstract: Introducing a suitable solution concept, we show that in bounded smooth domains $\Omega\subset \mathbb{R}n$, $n\ge 1$, the initial boundary value problem for the chemotaxis system \begin{align*} u_t&=\Delta u -\chi\nabla\cdot\left(\frac{u}{v}\nabla v\right)+\kappa u -\mu u2,\ v_t&=\Delta v -uv, \end{align*} with homogeneous Neumann boundary conditions and widely arbitrary initial data has a generalized global solution for any $\mu, \kappa, \chi >0$.

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