We propose a new numerical method for the solution of Bernoulli’s free boundary value problem for harmonic functions in a doubly connected domain D in R2 where an unknown free boundary Γ0 is determined by prescribed Cauchy data on Γ0 in addition to a Dirichlet condition on the known boundary Γ1. Our main idea is to involve the conformal mapping method as proposed and analyzed by Akduman, Haddar...

We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain Ω ⊂ Rn and we show that a Lipschitz stability estimate for the conductivity in terms of the local Dirichlet-to-Neumann map holds true.

in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime...

It is proved that the solution to exterior Neumann boundary value problem can be obtained as the limit of the solutions of some problems in the whole space. 1 Consider the following problem: (V' + k*)u =f in f2, ul,=O, where f2 = R3\D. D is bounded domain with a smooth boundary r, fE C,(Q), k > 0. In [l] we proved the following: THEOREM 1. Consider the problem V=N in D N = const. > 0. =0 in Q, ...

We study a Penrose-Fife phase transition model coupled with homogeneous Neumann boundary conditions. Improving previous results, we show that the initial value problem for this model admits a unique solution under weak conditions on the initial data. Moreover, we prove asymptotic regularization properties of weak solutions.

In this paper, a fourth-order nonlinear p-Laplacian difference equation is considered. Using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. The existing results are generalized and significantly complemented.

Parallelization of the algebraic ctitious domain method is considered for solving Neumann boundary value problems with variable coeecients. The resulting method is applied to the parallel solution of the subsonic full potential ow problem which is linearized by the Newton method. Good scalability of the method is demonstrated in Cray T3E distributed memory parallel computer using MPI in communi...

In this paper we study the equation ut = ∆[φ(u(x, [t/τ ]τ))u(x, t)] , x ∈ Ω , t > 0, with homogeneous Neumann boundary conditions in a bounded domain in R. We show existence and uniqueness for the initial value problem, and prove some results that show the aggregating behaviour exhibited by the solutions.

We study the inverse boundary value problem for the time-harmonic elastic waves. We focus on the recovery of the density and assume the sti↵ness tensor to be isotropic. The data are the Dirichlet-to-Neumann map. We establish a Lipschitz type stability estimate assuming that the density is piecewise constant with an underlying domain partitioning consisting of a finite number of subdomains.