We study here some linear elliptic partial differential equations (with Dirichlet, Fourier or mixed boundary conditions), to which convection terms (first order perturbations) are added that entail the loss of the classical coercivity property. We prove the existence, uniqueness and regularity results for the solutions to these problems. Mathematics Subject Classification (2000): 35J25.

Electrical Impedance Tomography (EIT) of closed conductive media is an ill-posed inverse problem. In order to solve the corresponding direct problem, the Finite Elements Method (FEM) provides good accuracy and preserves the non linear dependence of the observation set upon the conductivity distribution. In this paper, we show that the Bayesian approach presented in [1] for linear inverse imagin...

In this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. Almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. But we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as Legendre ...

This work provides a Linear Programming-based Polynomial Time Approximation Scheme (PTAS) for two classical NP-hard problems on graphs when the input graph is guaranteed to be planar, or more generally Minor Free. The algorithm applies a sufficiently large number (some function of 1/ when 1+ approximation is required) of rounds of the so-called Sherali-Adams Lift-and-Project system. needed to o...

Estimation problems for linear time-invariant systems with noisy input and output are considered. The smoothing problem is a least norm problem. An efficient algorithm using a Riccati-type recursion is derived. The equivalence between the optimal filter and an appropriately modified Kalman filter is established. The optimal estimate of the input signal is derived from the optimal state estimate...