Existence and uniqueness of solution for the nonlinear Brusselator system with Robin boundary conditions

The system of Brusselator-type reaction-diffusion equations (RDs) on open bounded convex domains 𝒟 ⊂ ℝ d {\mathcal{D}\subset\mathbb{R}^{d}} ( d ≤ 3 ) {(d\leq 3)} with Robin boundary conditions (Rbcs) has been mathematically analyzed. The Faedo–Galerkin approach is used to demonstrate the global existence and uniqueness of a weak solution to the system. The weak solution’s higher regularity findings are constructed under more regular conditions on the initial data. In addition, continuous dependence on the initial conditions has been proved.