Ageneral solution,basedontheseparationofvariablesmethod,for the thermal spreadingresistance incompound annular sectors, is presented. Results are given for three heat  ux distributions: inverse parabolic, uniform, and parabolic proŽ les. The general solution can be used to model any number of equally spaced heat sources on a compound or isotropic annulus. Graphical results are presented for a ...

In this paper, we suggest a method for recovering the unknown time-dependent strength of contaminant concentration source from measurements inside an unbounded domain. This problem is formulated as Cauchy parabolic inverse problem. For its efficient numerical processing, solved by reduction to Dirichet one on bounded domain using fundamental (potential) solutions in combination with adjoint equ...

In this article, simultaneous identification of the timewise lowest and source terms in a two-dimensional (2D) parabolic equation from knowledge additional measurements is studied. Existence uniqueness solution proved by means contraction mapping on small time interval. Since problem yet ill- posed (very errors time-average temperature input may cause large output potential functions), we need ...

We consider a 2×2 system of parabolic equations with first and zeroth coupling and establish a Carleman estimate by extra data of only one component without data of initial values. Then we apply the Carleman estimate to inverse problems of determining some or all of the coefficients by observations in an arbitrary subdomain over a time interval of only one component and data of two components a...

We consider the calibration of a Lévy process with American vanilla options. The price of an American vanilla option as a function of the maturity and the strike satisfies a forward in time linear complementarity problem involving a partial integro-differential operator. It leads to a variational inequality in a suitable weighted Sobolev space. Calibrating the Lévy process amounts to solving an...

This paper deals with the boundary value problem involving the differential equation begin{equation*}     ell y:=-y''+qy=lambda y,  end{equation*}  subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$  begin{equation*}     y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0), end{equation*} where $q(x),  a_1 , a_2$ are  rea...

Given an undirected network G(V,A,c) and a perfect matching M of G, the inverse maximum perfect matching problem consists of modifying minimally the elements of c so that M becomes a maximum perfect matching with respect to the modified vector. In this article, we consider the inverse problem when the modifications are measured by the weighted bottleneck-type Hamming distance. We propose an alg...