On a semilinear parabolic equation system with nonlocal and coupled boundary conditions (Q2726147)

Following the tracks of [\textit{C.-V. Pao}, Nonlinear parabolic and elliptic equations, Plenum Press, New York (1992; Zbl 0777.35001)], Wang Yuangdi and Zhou Shuqing study comparison principles for \(u_t-\Delta u= \varphi (u,v)\), \(v_t-\Delta v=\psi(u,v)\) in \(\Omega\times (0,T]\) under coupled boundary conditions, \(u(x,t)= \int_\Omega (\lambda_{11} (x,y)u(y,t) +\lambda_{1 2} (x,y)v(y,t))dy\) and \(v(x,t)= \int_\Omega (\lambda_{21} (x,y)u (y,t) + \lambda_{22} (x,y)v(y,t))dy\) on \(\partial\Omega \times(0,T]\). The basic assumption is that the coupling involved is quasimonotone nondecreasing or equivalent to quasimonotone nondecreasing.