Determining the boundary of a two-dimensional region from the solution of the external initial boundary-value problem for the heat equation |
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Authors: | S G Golovina A G Razborov |
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Institution: | (1) Department of Mathematics, Karlsruhe Institute of Technology (KIT), Kaiserstrasse 89, 76133 Karlsruhe, Germany |
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Abstract: | We determine the boundary of a two-dimensional region using the solution of the external initial boundary-value problem for
the nonhomogeneous heat equation. The initial values for the boundary determination include the right-hand side of the equation
and the solution of the initial boundary-value problem given for finitely many points outside the region. The inverse problem
is reduced to solving a system of two integral equations nonlinear in the function defining the sought boundary. An iterative
procedure is proposed for numerical solution of the problem involving linearization of integral equations. The efficiency
of the proposed procedure is investigated by a computer experiment. |
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