arXiv subjects

C. F. Portillo

Publications and source records attributed to C. F. Portillo.

3 recordsLinked to original sources

arXiv2019

On the Existence of Solution of the Boundary-Domain Integral Equation System derived from the 2D Dirichlet Problem for the Diffusion Equation with Variable Coefficient

A system of boundary-domain integral equations is derived from the bidimensional Dirichlet problem for the diffusion equation with variable coefficient using the novel parametrix from [22] different from the one in [5,18]. Mapping properties of the surface and volume parametrix based potential-type operators are analysed. Invertibility of the single layer potential is also studied in detail in appropriate Sobolev spaces. We show that the system of boundary-domain integral equations derived is equivalent to the Dirichlet problem prescribed and we prove the existence and uniqueness of solution in suitable Sobolev spaces of the system obtained by using arguments of compactness and Fredholm Alternative theory.

math.AP↗

arXiv2018

Analysis of Boundary-Domain Integral Equations based on a new parametrix for the mixed diffusion BVP with variable coefficient in an interior Lipschitz domain

A mixed boundary value problem for the partial differential equation of diffusion in an inhomogeneous medium in a Lipschitz domain is reduced to a system of direct segregated parametrix-based Boundary-Domain Integral Equations (BDIEs). We use a parametrix different from the one employed in the papers by Mikhailov (2002, 2006) and Chkadua, Mikhailov, Natroshvili (2009). We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed.

math.AP↗

arXiv2018

Analysis of Boundary-Domain Integral Equations to the Mixed BVP for a Compressible Stokes System with Variable Viscosity

The mixed boundary value problem for a compressible Stokes system of partial differential equations in a bounded domain is reduced to two different systems of segregated direct Boundary Integral Equations (BDIEs) expressed in terms of surface and volume parametrix-based potential type operators. Equivalence of the BDIE systems to the mixed BVP and invertibility of the matrix operators associated with the BDIE systems are proved in appropriate Sobolev spaces.

math.AP↗