In this paper we deal with some controllability problems for systems of the Navier– Stokes and Boussinesq kind with distributed controls supported in small sets. Our main aim is to control N-dimensional systems (N + 1 scalar unknowns in the case of the Navier–Stokes equations) with N − 1 scalar control functions. In a first step, we present some global Carleman estimates for suitable adjoint pr...

This paper presents the dynamic simulation model to characterize water pumping and heating installation using PV/Thermal panel (PV/T) is developed. The model consists of a set of mathematical equations governing the main components of the system; namely: transparent cover, solar cell, absorber plate and operating fluid. The model is based on the analysis of the energy balance which includes the...

Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations, are standard fare in the study of small amplitude surface waves in shallow water. While the shallow-water theory features conservation of mass, momentum and energy for smooth solutions, mechanical balance equations are not widely used in Boussinesq scaling, and it appears that the expressions for many of thes...

By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a BénardMarangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussines...

The study involves theoretical formulation, model development and verification, and integration with field observations of swash motions. The starting point of the theoretical formulation is the Euler equation of motion for waves and currents above the permeable seabed and the locally-averaged Navier-Stokes equations for the flow inside the porous layer. A complete set of fully nonlinear Boussi...

Trial equation method is a powerful tool for obtaining exact solutions of nonlinear differential equations. In this paper, the improved Boussinesq is reduced to an ordinary differential equation under the travelling wave transformation. Trial equation method and the theory of complete discrimination system for polynomial are used to establish exact solutions of the improved Boussinesq equation.