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The present paper deals with a nonlinear viscoelastic equation having a dissipation term. With the equation some classical and non classical boundary conditions are combined. Based on some a priori bounds, iteration processes and density arguments, we simultaneously solve the nonlinear and the associated linear problems.

Communicated by S. ChenThis paper deals with the solvability and uniqueness of a higher dimension mixed nonlocal problem for a Boussinesq equation. Galerkin's method was the main used tool for proving the solvability of the given nonlocal problem. Copyright

In this manuscript, we consider the fourth order of the Moore–Gibson–Thompson equation by using Galerkin’s method to prove the solvability of the given nonlocal problem.