A Second-order Hyperbolic Chemotaxis Model (Journal of Partial Differential Equations, 2019)
"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\u00a0 the method of characteristics and the contraction mapping principle."