Classical solutions to a logistic chemotaxis model with singular\n sensitivity and signal absorption

2018/03/11 by Elisa Lankeit, Lankeit, Elisa, Johannes Lankeit +1
Mathematics · #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.1803.04006

Abstract

Assuming that 0<\χ<\√ frac2n, \κ\≥ 0 and\n\μ>\(n-2)/(n), we prove global existence of classical solutions to a\nchemotaxis system slightly generalizing \
beginsplit u_t amp;=
Delta u -
chi\n
nabla
cdot (
fracuv
nabla v ) +
kappa u -
mu u²

v_t amp;=
Delta v - u\nv
endsplit in a bounded domain \Ω \⊂ \ℝⁿ, with\nhomogeneous Neumann boundary conditions and for widely arbitrary positive\ninitial data. In the spatially one-dimensional setting, we prove global\nexistence and, moreover, boundedness of the solution for any \χ>0, \μ>0,\n\κ\≥ 0.\n

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