Pseudoline arrangements and the Inverse Boundary Value Problem in Nonlinear Electrical Networks
نویسنده
چکیده
We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) conductors. For a fixed nonlinear electrical network, we show that under reasonable assumptions, there are well-defined Dirichletto-Neumann and Neumann-to-Dirichlet maps relating boundary voltages and boundary currents. We also generalize work of Curtis, Morrow, and others, characterizing the circular planar graphs for which the inverse boundary value problem has a solution, in the sense that the Dirichlet-to-Neumann maps determine all interior conductors.
منابع مشابه
AN INVERSE PROBLEM WITH UNKNOWN RADIATION TERM
In this paper, we consider an inverse problem of linear heat equation with nonlinear boundary condition. We identify the temperature and the unknown radiation tern from an overspecified condition on the boundary
متن کاملBoundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method
In this paper, we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain. This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve. To this end, the boundary integral equation method is used. Since the resulting system of linea...
متن کاملNumerical treatment for nonlinear steady flow of a third grade fluid in a porous half space by neural networks optimized
In this paper, steady flow of a third-grade fluid in a porous half space has been considered. This problem is a nonlinear two-point boundary value problem (BVP) on semi-infinite interval. The solution for this problem is given by a numerical method based on the feed-forward artificial neural network model using radial basis activation functions trained with an interior point method. ...
متن کاملInverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions
This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...
متن کاملNumerical quasilinearization scheme for the integral equation form of the Blasius equation
The method of quasilinearization is an effective tool to solve nonlinear equations when some conditions on the nonlinear term of the problem are satisfied. When the conditions hold, applying this technique gives two sequences of coupled linear equations and the solutions of these linear equations are quadratically convergent to the solution o...
متن کامل