Singular perturbation problems have been studied by many mathematicians. Since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. This paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

In the paper, we establish existence of steady boundary layer solution Boltzmann equation with specular condition in L 2 ∩L ∞ half-space. The uniqueness, continuity and exponential decay are obtained, such estimates important to prove Hilbert expansion for half-space problem condition.

abstract: since the field of micro electromechanical systems (mems) continues to grow, the flow in micro devices have become an area that receives a significant attention. the microscopic flows are usually characterized by the knudsen number (kn). when the characteristic size of the particle decreases down to a value comparable to the mean free path of the molecules, the continuum assumption fa...

the isogeometric analysis is increasingly used in various engineering problems. it is based on non-uniform rational b-splines (nurbs) basis function applied for the solution field approximation and the geometry description. one of the major concerns with this method is finding an efficient approach to impose essential boundary conditions, especially for inhomogeneous boundaries. the main contri...

We investigate a two-species competition model in advective homogeneous environments. assume that the two species are identical except their diffusion rates and advection rates. It is worth noting Neumann boundary condition assumed at upstream end, meanwhile, there always net loss of individuals incurred by water flow or both diffusive movements downstream end. Our results show when large (incu...

A square splittered and unsplittered rod is placed in a turbulent boundary layer developed over a flat plate. The effect of the resulting disturbances on the local heat transfer coefficient is then studied. In both cases the square rod modifies the flow structure inside the boundary layer. As a result, a stagnation point, a jet and wake area are generated around the square rod, each making a co...