TY - JOUR
T1 - Nonlinear Hyperbolic-parabolic System Modeling Some Biological Phenomena
AU - Shaohua Wu  & Hua Chen
JO - Journal of Partial Differential Equations
VL - 1
SP - 1
EP - 14
PY - 2011
DA - 2011/02
SN - 24
DO - http://doi.org/10.4208/jpde.v24.n1.1
UR - https://global-sci.org/intro/article_detail/jpde/5194.html
KW - Hyperbolic-parabolic system
KW - chemosensitive movement
KW - external signal
KW - global existence
AB - <p>In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N=1, the global existence of the weak solution will be established by the bootstrap argument.</p>