Blow-up of a nonlinear reaction–diffusion system with nonlocal weighted exponential boundary condition

In this paper, we study a class of reaction–diffusion system with nonlinear terms, variable coefficients, and nonlocal exponential boundary conditions. We demonstrate the existence of solutions using the subsolution and supersolution method, comparison principle, and representation theorem. Uniqueness of solutions is established via the contraction mapping principle, aided by the Green’s function. Furthermore, we construct supersolutions to prove the existence of global solutions under various conditions. By employing the auxiliary function method, we obtain upper and lower bounds for blow-up solutions under different parametric settings. Finally, examples are provided to verify our theoretical findings.