Starting from a model of traffic congestion, we introduce a minimal-flow–like variational problem whose solution is characterized by a very degenerate elliptic PDE. We precisely investigate the relations between these two problems, which can be done by considering some weak notion of flow for a related ODE. We also prove regularity results for the degenerate elliptic PDE, which enables us in so...

in this paper, a numerical method is developed for solving a linear sixth order boundaryvalue problem (6vbp ) by using the hyperbolic uniform spline of order 3 (lower order). thereis proved to be first-order convergent. numerical results confirm the order of convergencepredicted by the analysis.

in this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. we prove a posteriori $ l^2(l^2)$ and error estimates for this method under minimal regularity hypothesis. test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

In the earlier paper [6] a Galerkin method was proposed and analyzed for the numerical solution of a Dirichlet problem for a semi-linear elliptic boundary value problem of the form U = F ( ; U). This was converted to a problem on a standard domain and then converted to an equivalent integral equation. Galerkin’s method was used to solve the integral equation, with the eigenfunctions of the Lapl...

IT is intuitively obvious that if a simple continuous curve is given in the (x, 2/)-plane, and a continuous distribution of values along the curve, there will exist functions of x and y which are continuous in both variables together, and which take on the prescribed values along the curve. It is the purpose of the present note to give an analytic proof of this fact, by elementary means, and, i...

In this paper we consider an inverse boundary value problem of determining three dimensional unknown inclusions in an elliptic equation in a bounded domain Ω ⊂ R3 from finite boundary measurements on ∂Ω. We will show that polyhedral inclusions in Ω can be uniquely determined up to their convex edges from a single boundary measurement on ∂Ω.

The usual way to model heat conduction is to solve a partial differential equation (PDE) with boundary conditions (BCs), i.e., a boundary value problem (BVP). For the case of steady-state heat conduction in a homogeneous isotropic solid with thermal conductivity independent of temperature and with no heat source inside the solid, temperature T (x, y, z) in the solid verifies Laplace equation [5] :