期刊论文详细信息
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 卷:434
Global existence and asymptotic stability of smooth solutions to a fluid dynamics model of biofilms in one space dimension
Article
Bianchini, Roberta1  Natalini, Roberto2 
[1] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci 1, I-00193 Rome, Italy
[2] CNR, Ist Applicaz Calcolo M Picone, Via Taurini 19, I-00181 Rome, Italy
关键词: Fluid dynamics models;    Dissipative hyperbolic equations;    Biofilms;    Global existence;    Asymptotic stability;   
DOI  :  10.1016/j.jmaa.2015.10.014
来源: Elsevier
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【 摘 要 】

In this paper, we present an analytical study, in the one space dimensional case, of the fluid dynamics system proposed in [3] to model the formation of biofilms. After showing the hyperbolicity of the system, we show that, in an open neighborhood of the physical parameters, the system is totally dissipative near its unique non-vanishing equilibrium point. Using this property, we are able to prove existence and uniqueness of global smooth solutions to the Cauchy problem on the whole line for small perturbations of this equilibrium point and the solutions are shown to converge exponentially in time at the equilibrium state. (C) 2015 Elsevier Inc. All rights reserved.

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