Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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  • J. Lankeit

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OriginalspracheEnglisch
Seiten (von - bis)4052-4084
Seitenumfang33
FachzeitschriftJournal of differential equations
Jahrgang262
Ausgabenummer7
PublikationsstatusVeröffentlicht - 2017

Abstract

We show the existence of locally bounded global solutions to the chemotaxis system {u t=∇⋅(D(u)∇u)−∇⋅([formula presented]∇v)in Ω×(0,∞)v t=Δv−uvin Ω×(0,∞)∂ νu=∂ νv=0in ∂Ω×(0,∞)u(⋅,0)=u 0,v(⋅,0)=v 0in Ω in smooth bounded domains Ω⊂R N, N≥2, for D(u)≥δu m−1 with some δ>0, provided that m>1+[formula presented].

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Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion. / Lankeit, J.
in: Journal of differential equations, Jahrgang 262, Nr. 7, 2017, S. 4052-4084.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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N2 - We show the existence of locally bounded global solutions to the chemotaxis system {u t=∇⋅(D(u)∇u)−∇⋅([formula presented]∇v)in Ω×(0,∞)v t=Δv−uvin Ω×(0,∞)∂ νu=∂ νv=0in ∂Ω×(0,∞)u(⋅,0)=u 0,v(⋅,0)=v 0in Ω in smooth bounded domains Ω⊂R N, N≥2, for D(u)≥δu m−1 with some δ>0, provided that m>1+[formula presented].

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