Boundedness in the higher-dimensional attraction-repulsion chemotaxis system involving tensor-valued sensitivity with saturation

作者：Yi, Hong^*; Mu, Chunlai; Li, Dan; Qiu, Shuyan

来源：MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44(6): 4541-4559.

DOI：10.1002/mma.7049

• boundedness
• chemotaxis
• logistic source
• nonlinear diffusion
• tensor-valued sensitivity

In this paper, we consider the attraction-repulsion parabolic-parabolic-parabolic model with nonlinear diffusion @@@ {u(t) = del center dot(D(u) del u)- del center dot(uS(1)(x,u,v) del v)+ del center dot(uS(2)(x,u,w) del w) @@@ +xi u - mu u(2), x is an element of Omega,t>0, @@@ v(t) = Delta v+alpha u-beta v, x is an element of Omega,t>0, @@@ w(t)=Delta w+gamma u-delta w,x is an element of Omega,t>0, @@@ in a smooth bounded domain Omega subset of R-n(n >= 2), where alpha, beta, gamma, delta, mu are given positive parameters and xi >= 0. The function D satisfies D(u) >= C(D)u(m - 1) for all u > 0 with C-D > 0. S-i(i=1,2) are given matrix-valued functions in R-nxn which fulfill @@@ |S-1(x,u,v)|<= C-S1(1+u)(-alpha 1),|S-2(x,u,w)|<= C-S2(1+u)(-alpha 2) @@@ with some C-Si>0 and alpha(i)>0(i=1,2). It is shown that under the conditions m > 0 and min{m+2 alpha(1),m+2 alpha(2)}>2n/n+2, the corresponding initial boundary value problem possesses at least one global bounded weak solution.

• 单位
  重庆大学