In this paper the optimal control of boundary heat flux in a 2-D solid body with an arbitrary shape is performed in order to achieve the desired temperature distribution at a given time interval. The boundary of the body is subdivided into a number of components. On each component a time-dependent heat flux is applied which is independent of the others. Since the thermophysical properties are t...

In this work, the least squares weighted residual method is used to solve the two-dimensional (2D) elasticity problem of a rectangular plate of in-plane dimensions 2a 2b subjected to parabolic edge tensile loads applied at the two edges x = a. The problem is expressed using Beltrami–Michell stress formulation. Airy’s stress function method is applied to the stress compatibility equation, and th...

This paper is concerned with the boundary layer problem on a chemotaxis system modelling formation of aerobic bacteria in fluid. Completing physical Robin-type conditions for oxygen and no-flux bacteria, we show that gradients its radial solutions region between two concentric spheres possessing effects as diffusion rate $ \varepsilon goes to zero boundary-layer thickness order \mathcal{O}(\var...

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

In this paper, an impulsive boundary value problem on the half-line is considered and existence of solutions is proved using Minimization Principal and Mountain Pass Theorem.