TY - JOUR
T1 - A Second-order Hyperbolic Chemotaxis Model
AU - Wu , Shaohua
AU - Chen , Haiying
JO - Journal of Partial Differential Equations
VL - 3
SP - 269
EP - 280
PY - 2019
DA - 2019/10
SN - 32
DO - http://doi.org/10.4208/jpde.v32.n3.4
UR - https://global-sci.org/intro/article_detail/jpde/13342.html
KW - Chemotaxis model
KW - hyperbolic equations
KW - correlated random walks.
AB - <p>In this paper, we study a hyperbolic type chemotaxis model in one space dimension. We assume the speed is constant, the production and degradation of the external signal $s$ is given by \mbox{$-\beta s+f(u^++u^-)$,} where $f(u^++u^-)$ is the general form and $u^+, u^-$ depend on $s$. The existence of the weak solution of the model considered in the paper is obtained by&nbsp; the method of characteristics and the contraction mapping principle.</p>