A NEW CRITERION TO A TWO-CHEMICAL SUBSTANCES CHEMOTAXIS SYSTEM WITH CRITICAL DIMENSION

作者：Bai, Xueli^*; Liu, Suying

来源：Discrete and Continuous Dynamical Systems-Series B, 2018, 23(9): 3717-3721.

DOI：10.3934/dcdsb.2018074

• New criterion
• chemotaxis
• critical dimension
• global boundedness
• interpolation inequality

We mainly investigate the global boundedness of the solution to the following system,
{u(t) = Delta u - chi Delta . (u del v) in Omega x R+,
v(t) = Delta v - v + w in Omega x R+,
w(t) = Delta w - w + u in Omega R+,
under homogeneous Neumann boundary conditions with nonnegative smooth initial data in a smooth bounded domain Omega subset of R-n with critical space dimension n = 4. This problem has been considered by K. Fujie and T. Senba in [5]. They proved that for the symmetric case the condition integral(Omega) u(0) < (8 pi)(2)/chi yields global boundedness, where u(0) is the instal data for u. In this paper, inspired by some new techniques established in [3], we give a new criterion for global boundedness of the solution. As a byproduct, we obtain a simplified proof for one of the main results in [5].

• 出版日期2018-11
• 单位西北工业大学