Geodesic
Some Inverse Problems for Mathematical Models of Heat and Mass Transfer
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 4, pp. 63-72 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the article we consider well-posedness questions of inverse problems for mathematical models of heat and mass transfer. We recover a solution of a parabolic equation of the second order and a coefficient in this equation characterizing parameters of a medium and belonging to the kernel of a differential operator of the first order with the use of data of the first boundary value problem and the additional Neumann condition on the lateral boundary of a cylinder (thereby we have the Cauchy data on the lateral boundary of a cylinder). An unknown coefficient can occur in the main part of the equation. A solution is sought in a Sobolev space with sufficiently large summability exponent and an unknown coefficient in the class of continuous functions. The problem is shown to have a unique stable solution locally in time.
Keywords: inverse problem; heat and mass transfer; boundary value problem; parabolic equation; well-posedness; diffusion. 
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S. G. Pyatkov; A. G. Borichevskaya. Some Inverse Problems for Mathematical Models of Heat and Mass Transfer. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 4, pp. 63-72. http://geodesic.mathdoc.fr/item/VYURU_2013_6_4_a6/

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