we consider a mixed boundary value problem for a quarter-plane with a robin condition on one edge. we have developed two procedures, one based on the advanced theory of dual integral equations and the other, in our opinion simpler technique, relying on conformal mapping. both of the procedures are of interest, because the former may be easier to adapt to other boundary value problems.

We consider a mixed boundary value problem for a quarter-plane with a Robin condition on one edge. We have developed two procedures, one based on the advanced theory of dual integral equations and the other, in our opinion simpler technique, relying on conformal mapping. Both of the procedures are of interest, because the former may be easier to adapt to other boundary value problems.

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

the aim of this paper is to introduce a new approach for obtaining the numerical solution of singulary perturbed boundary value problems based on an optimal control technique. in the proposed method, first the mentioned equations are converted to an optimal control problem. then, control and state variables are approximated by chebychev series. therefore, the optimal control problem is reduced ...