2 research outputs found
On a mixed problem for the parabolic Lam'e type operator
We consider a boundary value problem for the parabolic Lam\'e type operator
being a linearization of the Navier-Stokes' equations for compressible flow of
Newtonian fluids. It consists of recovering a vector-function, satisfying the
parabolic Lam\'e type system in a cylindrical domain, via its values and the
values of the boundary stress tensor on a given part of the lateral surface of
the cylinder. We prove that the problem is ill-posed in the natural spaces of
smooth functions and in the corresponding H\"older spaces; besides, additional
initial data do not turn the problem to a well-posed one. Using the Integral
Representation's Method we obtain the Uniqueness Theorem and solvability
conditions for the problem
Representations and symbolic computation of generalized inverses over fields
This paper investigates representations of outer matrix inverses with prescribed range and/or none space in terms of inner inverses. Further, required inner inverses are computed as solutions of appropriate linear matrix equations (LME). In this way, algorithms for computing outer inverses are derived using solutions of appropriately defined LME. Using symbolic solutions to these matrix equations it is possible to derive corresponding algorithms in appropriate computer algebra systems. In addition, we give sufficient conditions to ensure the proper specialization of the presented representations. As a consequence, we derive algorithms to deal with outer inverses with prescribed range and/or none space and with meromorphic functional entries.Agencia Estatal de investigaciónUniversidad de Alcal