it is well known that the parabolic partial differential equationsin two or more space dimensions with overspecified boundary data,feature in the mathematical modeling of many phenomena. in thisarticle, an inverse problem of determining an unknowntime-dependent source term of a parabolic equation in generaldimensions is considered. employing some transformations, wechange the inverse problem to...

In this paper the optimal control of boundary heat flux in a 2-D solid body with an arbitrary shape is performed in order to achieve the desired temperature distribution at a given time interval. The boundary of the body is subdivided into a number of components. On each component a time-dependent heat flux is applied which is independent of the others. Since the thermophysical properties are t...

in this paper the optimal control of boundary heat flux in a 2-d solid body with an arbitrary shape is performed in order to achieve the desired temperature distribution at a given time interval. the boundary of the body is subdivided into a number of components. on each component a time-dependent heat flux is applied which is independent of the others. since the thermophysical properties are t...

The problem of interest in this article is to study the (non-local) inverse recovering a potential based on boundary measurement associated with fractional Schrödinger equation. Let $0\<a<1$, and let $u$ solve $$ \begin{cases} ((-\Delta)^a + q )u = 0 &\operatorname{in} \Omega,\ \operatorname{supp}, u\subseteq \overline{\Omega}\cup \overline{W} ,\ \cap \overline{\Omega}=\emptyset. \end{cases} We...

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. ...

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...