Time delayed parabolic systems with coupled nonlinear boundary conditions (Q2781255)

The paper deals with time-delayed parabolic equations on a bounded domain \(\Omega\) in \(\mathbb{R}^n\) with coupled nonlinear boundary conditions. Time delays may appear both in reaction term and the boundary condition. Existence and uniqueness of a solution is shown by using upper and lower solutions and nonquasimonotone functions, generalising, among others, the author's earlier results in [J. Math. Anal. Appl. 196, No. 1, 237-265 (1995; Zbl 0854.35122); 205, No. 1, 157-185 (1997; Zbl 0880.35126)]. A two-compartment model of genetic repression is briefly mentioned as an example.