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<p>In this paper, we consider the question on the well-posedness in Sobolev spaces of the problem of determining the source function in a heat and mass transfer system consisting of the Navier–Stokes system, a parabolic equation for temperature, and a parabolic system for the concentrations of substances being transferred. Weighted integrals of solutions over the spatial domain serve as overdetermination conditions. A local (in time) existence theorem for the solution of the problem in the nonlinear case is proved and stability estimates are obtained; for a linearized system, a global existence theorem is obtained.</p>

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On Some Classes of Inverse Problems on Determining Source Functions for Heat and Mass Transfer Systems

  • 期刊论文

  • 发表日期：

    2025年2月26日

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  • S. G. Pyatkov

摘要

In this paper, we consider the question on the well-posedness in Sobolev spaces of the problem of determining the source function in a heat and mass transfer system consisting of the Navier–Stokes system, a parabolic equation for temperature, and a parabolic system for the concentrations of substances being transferred. Weighted integrals of solutions over the spatial domain serve as overdetermination conditions. A local (in time) existence theorem for the solution of the problem in the nonlinear case is proved and stability estimates are obtained; for a linearized system, a global existence theorem is obtained.