HIV evolution model that describes the dynamics of concentrations of uninfected and infected cells is considered in the paper. The introduction of dimensionless variables and parameters leads to the initial boundary value problem for singularly perturbed system of partial integro-differential equations. By Tikhonov-Vasil’eva boundary functions method asymptotic solution with boundary layer is c...

In this paper, we study the global exisitence of L∞ weak entropy solution to the initial boundary value problem for compressible Euler equations with relaxtion and the large time asymptotic behavior of the solution. Motivated by the sub-characterisitic conditions, we proposed some structural conditions on the relaxation term comparing with the pressure function. These conditions are proved to b...

We construct global L∞ entropy weak solutions to the initial boundary value problem for the damped compressible Euler equations on bounded domain with physical boundaries. Time asymptotically, the density is conjectured to satisfy the porous medium equation and the momentum obeys to the classical Darcy’s law. Based on entropy principle, we showed that the physical weak solutions converges to st...

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...

In this paper we study of collocation method with Radial Basis Function to solve one dimensional time dependent Schrodinger equation in an unbounded domain. To this end, we introduce artificial boundaries and reduce the original problem to an initial boundary value problem in a bounded domain with transparent boundary conditions that involves half order fractional derivative in t. Then in three...

In this paper we focus on the initial-boundary value problem of the 2-D isentropic Euler equations with damping. We prove the global-intime existence of classical solution to the initial-boundary value problem by the method of energy estimates. keywords: Euler equation; initial-boundary value problem; well-posedness. MSC(2000): 35A05; 35L45.

due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. in this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on gurtin-murdoch continuum model to consider surface stre...