Mathematische Nachrichten

Boundedness in a fully parabolic chemotaxis‐consumption system with nonlinear diffusion and sensitivity, and logistic source

Early View

Abstract

In this paper we study the zero‐flux chemotaxis‐system

Ω being a convex smooth and bounded domain of R n , n 1 , and where m , k R , μ > 0 and α < m + 1 2 . For any v 0 the chemotactic sensitivity function is assumed to behave as the prototype χ ( v ) = χ 0 ( 1 + a v ) 2 , with a 0 and χ 0 > 0 . We prove that for nonnegative and sufficiently regular initial data u ( x , 0 ) and v ( x , 0 ) , the corresponding initial‐boundary value problem admits a unique globally bounded classical solution provided μ is large enough.

Related Topics

Related Publications

Related Content

Site Footer

Address:

This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on StatisticsViews.com are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and StatisticsViews.com express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.