arXiv subjects

Jean Ghislain Compaore

Publications and source records attributed to Jean Ghislain Compaore.

3 recordsLinked to original sources

arXiv2015

Solving Navier-Stokes equations coupled with a heat transfer equation using Bagarello's approach and the Hankel transform

In this paper, the dynamics of an incompressible fluid in a bounded connected domain, described by Navier-Stokes equations coupled with a heat transfer equation, is investigated by a method inspired from the non-commutative strategy developed by Bagarello, (see Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394).The solution of involved systems of partial differential equations is derived with the help of the unbounded self-adjoint densely defined Hamiltonian operator of the physical model and the Hankel transform.

math-ph↗

arXiv2015

Control of ordinary differential equations using Bagarello's operator approach : Case of forced harmonic oscillator systems

This work deals with the study of an optimal control of a system of nonlinear differential equations using the Bagarello's operator approach, recently introduced in a paper (Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394). The control problem is reduced by using the Pontryagin's maximum principle, to a system of ordinary differential equations with unknown state and adjoint variables. Its solution is then described in terms of a series expansion of commutators involving an unbounded self-adjoint, densely defined, system Hamiltonian operator H and initial position operators. Relevant simple applications are discussed.

math-ph↗

arXiv2015

Generalizing Bagarello's operator approach to solve a class of partial differential equations

The non-commutative strategy developed by Bagarello (see Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394) for the analysis of systems of ordinary differential equations (ODEs) is extended to a class of partial differential equations (PDEs), namely evolution equations and Navier-Stokes equations. Systems of PDEs are solved using an unbounded self-adjoint, densely defined, Hamiltonian operator and a recursion relation which provides a multiple commutator and a power series solution. Numerous examples are given in this work.

math-ph↗