on the basis of a reproducing kernel space, an iterative algorithm for solving the inverse problem for heat equation with a nonlocal boundary condition is presented. the analytical solution in the reproducing kernel space is shown in a series form and the approximate solution vn is constructed by truncating the series to n terms. the convergence of vn to the analytical solution is also proved. ...

The paper proposes  algorithms  for  numerical  solving  an  inverse  problem for a mixed parabolic-hyperbolic type equation with nonlocal condition finding the right-hand side of equation. It was assumed that function included in and is additional information solving inverse may be known some error, since they are result practical measurements. Three algorith...

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which ten...

Abstract In this paper, the general and supplementary conditions are used to determine inverse heat conduction in parabolic equation. The measured ensure that problem has a unique solution, but solution is not stable, so ill-posed. Using boundary element method discretize original problem, it solve problem. On basis, direct method, least square regular tried. Finally, minimal energy system. Num...

Let ut −∇2u = f(x) := ∑M m=1 amδ(x− xm) in D × [0,∞), where D ⊂ R3 is a bounded domain with a smooth connected boundary S, am = const, δ(x− xm) is the delta-function. Assume that u(x, 0) = 0, u = 0 on S. Given the extra data u(yk, t) := bk(t), 1 ≤ k ≤ K, can one find M,am, and xm? Here K is some number. An answer to this question and a method for finding M,am, and xm are given.

<p style='text-indent:20px;'>In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability the involving simultaneous recovery of two source terms from single measurement and interior observations, based on recent Carleman estimate such problems.</p>

We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations dynamic boundary conditions. prove a Lipschitz stability estimate for relevant potentials using recent Carleman estimate, and logarithmic result by convexity method, based on observations arbitrary subdomain.