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- W2953550647 abstract "This paper deals with a lower bound for the blow-up time for solutions of the fully parabolic chemotaxis system{ut=∇⋅[(u+α)m1−1∇u−χu(u+α)m2−2∇v]inΩ×(0,T),vt=Δv−v+uinΩ×(0,T) under Neumann boundary conditions and initial conditions, where Ω is a general bounded domain in Rn with smooth boundary, α>0, χ>0, m1,m2∈R and T>0. Recently, Anderson–Deng [1] gave a lower bound for the blow-up time in the case that m1=1 and Ω is a convex bounded domain. The purpose of this paper is to generalize the result in [1] to the case that m1≠1 and Ω is a non-convex bounded domain. The key to the proof is to make a sharp estimate by using the Gagliardo–Nirenberg inequality and an inequality for boundary integrals. As a consequence, the main result of this paper reflects the effect of nonlinear diffusion and need not assume the convexity of Ω." @default.
- W2953550647 created "2019-07-12" @default.
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- W2953550647 date "2019-11-01" @default.
- W2953550647 modified "2023-10-18" @default.
- W2953550647 title "Effect of nonlinear diffusion on a lower bound for the blow-up time in a fully parabolic chemotaxis system" @default.
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- W2953550647 doi "https://doi.org/10.1016/j.jmaa.2019.06.068" @default.
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