Monotone Iterative Algorithms for Coupled Systems of Nonlinear Parabolic Boundary Value Problems

Let us consider the following coupled system of nonlinear parabolic equations (1) ∂ u s / ∂ t − L ( s ) u s + g ( s ) ( t , x , u s ) ⋅ ∇ u s = f ( s ) ( t , x , u 1 , u 2 ) ,     s = 1 , 2 ,   ( t ∈ ( 0 , T ] ,   x ∈ Ω ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072140/faeac70b-e389-4ea4-8b5b-5a836c2a1f73/content/eq1065.tif"/> ,