This analysis shows the existence and uniqueness of solutions for the long wave equation, indicating effectiveness of the Faedo-Galerkin method.
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.
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Sadiq et al. (2025) studied this question.
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