Geodesic
Inverse problem for a linearized quasi-stationary phase field model with degeneracy
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 2, pp. 128-132

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The inverse problem for a linearized quasi-stationary phase field model is considered. The inverse problem is reduced to a linear inverse problem for the first order differential equation in a Banach space with a degenerate operator at the derivative and an overdetermination condition on the degeneracy subspace. The unknown parameter in the problem dependens on the source time function. The theorem of existence and uniqueness of classical solutions is proved by methods of degenerate operator semigroup theory at some additional conditions on the operator. General results are applied to the original inverse problem.
Keywords: inverse problem, phase field model, degenerate operator, operator semigroup, Banach spaces.
Mots-clés : Sobolev type equation 
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     title = {Inverse problem for a linearized quasi-stationary phase field model with degeneracy},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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     publisher = {mathdoc},
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N. D. Ivanova. Inverse problem for a linearized quasi-stationary phase field model with degeneracy. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 2, pp. 128-132. http://geodesic.mathdoc.fr/item/VYURU_2013_6_2_a9/