Some inverse problems for convection-diffusion equations

S. G. Pyatkov   ; E. I. Safonov

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 4, pp. 36-50

Résumé

We examine the well-posedness questions for some inverse problems in the mathematical models of heat-and-mass transfer and convection-diffusion processes. The coefficients and right-hand side of the system are recovered under certain additional overdetermination conditions, which are the integrals of a solution with weights over some collection of domains. We prove an existence and uniqueness theorem, as well as stability estimates. The results are local in time. The main functional spaces used are Sobolev spaces. These results serve as the base for justifying of the convergence of numerical algorithms for inverse problems with pointwise overdetermination, which arise, in particular, in the heat-and-mass transfer problems on determining the source function or the parameters of a medium.

Détail

Keywords: parabolic system; convection-diffusion; heat-and-mass transfer; inverse problem; control problem; boundary value problem; well-posedness.

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