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
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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.
@article{VYURU_2013_6_4_a6,
author = {S. G. Pyatkov and A. G. Borichevskaya},
title = {Some {Inverse} {Problems} for {Mathematical} {Models} of {Heat} and {Mass} {Transfer}},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
pages = {63--72},
publisher = {mathdoc},
volume = {6},
number = {4},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VYURU_2013_6_4_a6/}
}
TY - JOUR AU - S. G. Pyatkov AU - A. G. Borichevskaya TI - Some Inverse Problems for Mathematical Models of Heat and Mass Transfer JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie PY - 2013 SP - 63 EP - 72 VL - 6 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VYURU_2013_6_4_a6/ LA - ru ID - VYURU_2013_6_4_a6 ER -
%0 Journal Article %A S. G. Pyatkov %A A. G. Borichevskaya %T Some Inverse Problems for Mathematical Models of Heat and Mass Transfer %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie %D 2013 %P 63-72 %V 6 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/VYURU_2013_6_4_a6/ %G ru %F VYURU_2013_6_4_a6
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/