Analysis of class of 2D nonlinear Rosenau-regularized long wave equation with Neumann boundary conditions

We analyze nonlinear Rosenau-Regularized LongWave equation on open bounded convex domains with Neumann boundary conditions. The classical Faedo-Galerkin method, combined with compactness arguments, is employed to establish the existence, continuous dependence and uniqueness of analytic solutions on the initial data. Furthermore, a comprehensive case study is presented to illustrate the application of this approach to the Rosenau equation.