A quasilinear problem with large diffusion and nonlinear dynamic boundary conditions

This paper concerns quasilinear parabolic equations with p-Laplacian and q-Laplacian–Beltrami principal operators, subject to nonlinear dynamic boundary conditions. We examine the effect of large diffusion on the system, which leads to spatial homogenization. We establish the well-posedness of the perturbed problem and prove that, as the diffusion coefficients become large, the solution converges to that of a limiting system of ordinary differential equations. Additionally, we demonstrate the upper semicontinuity of the attractors, showing their converge to the limiting attractor as the parameter ε ε tends to zero.