Geodesic
On the solution of inverse problems for generalized oxygen consumption
Applications of Mathematics, Tome 46 (2001) no. 2, pp. 145-155 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We present the solution of some inverse problems for one-dimensional free boundary problems of oxygen consumption type, with a semilinear convection-diffusion-reaction parabolic equation. Using a fixed domain transformation (Landau’s transformation) the direct problem is reduced to a system of ODEs. To minimize the objective functionals in the inverse problems, we approximate the data by a finite number of parameters with respect to which automatic differentiation is applied.
We present the solution of some inverse problems for one-dimensional free boundary problems of oxygen consumption type, with a semilinear convection-diffusion-reaction parabolic equation. Using a fixed domain transformation (Landau’s transformation) the direct problem is reduced to a system of ODEs. To minimize the objective functionals in the inverse problems, we approximate the data by a finite number of parameters with respect to which automatic differentiation is applied.
DOI : 10.1023/A:1013735806210
Classification : 35K55, 35R30, 35R35, 49M15, 49N45, 49N50, 65M32
Keywords: oxygen consumption; inverse problems; automatic differentiation 
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     title = {On the solution of inverse problems for generalized oxygen consumption},
     journal = {Applications of Mathematics},
     pages = {145--155},
     year = {2001},
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Constales, D.; Kačur, J. On the solution of inverse problems for generalized oxygen consumption. Applications of Mathematics, Tome 46 (2001) no. 2, pp. 145-155. doi: 10.1023/A:1013735806210

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