Global Well-posedness and Dynamics of Two-component Reaction-diffusion Systems with Arbitrary-growing Nonlinearities

Abstract

This work investigates the global well-posedness and long-term dynamics of two-component reaction-diffusion systems on bounded domains under homogeneous Dirichlet boundary conditions. We introduce a weaker dissipative condition that enables us to prove the global existence and uniqueness of classical solutions to the associated Cauchy problem, without imposing any growth constraints on the nonlinear terms. The admissible nonlinearities include, but are not limited to, polynomial and exponential growth types. Furthermore, we demonstrate that such systems admit both global and exponential attractors, which exhibit finite-dimensional characteristics in appropriate continuous function spaces.