Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities

This paper studies time-periodic solutions of singularly perturbed Tikhonov systems of reaction–diffusion–advection equations with nonlinearities that include the square of the gradient of the unknown function (KPZ nonlinearities). The boundary layer asymptotics of solutions are constructed for Neumann and Dirichlet boundary conditions. The study considers both the case of quasimonotone sources and systems without the quasimonotonicity condition. The asymptotic method of differential inequalities is used to prove theorems on the existence of solutions and their Lyapunov asymptotic stability. DOI 10.1134/S1061920824030129