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
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.
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.
This paper is concerned with a problem of a logarithmic nonuniform flexible structure with time delay, where the heat flux is given by Cattaneo’s law. We show that the energy of any weak solution blows up infinite time if the initial energy is negative.
In this paper, we study the elastic membrane equation with dynamic boundary conditions, source term and a nonlinear weak damping localized on a part of the boundary and past history. Under some appropriate assumptions on the relaxation function the general decay for the energy have been established using the perturbed Lyapunov functionals and some properties of convex functions.
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