Some classes of inverse evolution problems for parabolic equations

We consider the problem of simultaneously determining coefficients of a second order nonlinear parabolic equation and a solution to this equation. The unknown coefficients occur in the main part and in the nonlinear summand as well. The overdetermination conditions are conditions of the Dirichlet ty...

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Bibliographic Details
Published in:Siberian mathematical journal 2009, Vol.50 (1), p.141-153
Main Authors: Pyatkov, S. G., Tsybikov, B. N.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We consider the problem of simultaneously determining coefficients of a second order nonlinear parabolic equation and a solution to this equation. The unknown coefficients occur in the main part and in the nonlinear summand as well. The overdetermination conditions are conditions of the Dirichlet type on a family of planes of arbitrary dimension. It is demonstrated that the problem in question is solvable locally in time in Hölder spaces. When the unknown functions enter the right-hand side and the equation is linear, the theorem of global unique existence (in time) is established.
ISSN:0037-4466
1573-9260
DOI:10.1007/s11202-009-0016-5