Blow-Up Profiles for a Semilinear Chemotaxis System Arising in Biology

  • Rong-Nian Wang

    Shanghai Normal University, China
  • Tao Wang

    Nanchang University, China
  • Yong Zhou

    Xiangtan University, Xiangtan, Hunan, China

Abstract

We consider the semilinear coupled system of parabolic-elliptic partial di erential equations arising in chemotaxis involving forcing source of exponential growth type and homogeneous Dirichlet boundary conditions. The local existence and uniqueness of nonnegative classical solutions are proved. Also, a lower bound for the blow-up time if the solution blows up in nite time is derived. Moreover, the exponential decay of the associated energies are also studied. The results we obtained here essentially extend some existing results in this area.

Cite this article

Rong-Nian Wang, Tao Wang, Yong Zhou, Blow-Up Profiles for a Semilinear Chemotaxis System Arising in Biology. Z. Anal. Anwend. 33 (2014), no. 4, pp. 417–428

DOI 10.4171/ZAA/1519