On the higher dimension Boussinesq equation with nonclassical condition

Abstract

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

On the numerical solution of a singular second-order thermoelastic system

“…For more details, see literature. [19][20][21] We first establish a priori estimate for the solution from which the uniqueness of the solution follows. Then, based on the density of the range of the operator generated by the problem in consideration, we prove the existence of the solution of problems (1) À (3).…”

“…where N i are known operators and u i (x, t) are unknown functions. Then, the zeroth-order deformation equations for system (20) are…”

Galerkin method for nonlocal mixed boundary value problem for the Moore‐Gibson‐Thompson equation with integral condition

“…Too many physical phenomena are modeled by initial boundary value problems for second-order evolutions partial differential equations (a = 0) with nonlocal constraints such as integral boundary conditions, where the data cannot be measured directly on the boundary, but the average value of the solution on the domain is known, this problems can be encountered in many scientific domains and many engineering models, see previous works. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] Mesloub and Mesloub 25 have applied the Galerkin method to a higher dimension mixed nonlocal problem for a Boussinesq equation and established the solvability, uniqueness of a weak solution.…”

On Some Initial and Initial Boundary Value Problems for Linear and Nonlinear Boussinesq Models

“…During the last three decades, many methods have been developed and used to solve these equations, such as homotopy analysis and homotopy perturbation methods (Francisco and Fernández [6], Gupta and Saha [7] and Dianhen et al [8]), the analytic method [9], the modified decomposition method (Wazwaz [10], Fang et al [11] and Basem and Attili [12]) the Laplace Adomian Decomposition Method (Hardik et al [13], Zhang et al [14], Liang et al [15]) the transformed rational function method (Wang [16], Engui [17]) the integral transform method (Charles et al [18]) the energy integral method (Joseph [19], Mesloub [20]) the inverse scattering method (Peter et al [21]) and other different numerical methods were used to investigate problems dealing with Boussinesq equations, see for example, Jang [22], Iskandar and Jain [23], Bratsos [24], Dehghan and Salehi [25], Boussinesq [26], and Onorato et al [27]. For the bifurcation of solutions and possible applications of Boussinesq equations, we may refer to References [28,29].…”