Abstract
After describing the technical background that led to the inverse problem for a nonlinear heat equation considered in this paper, we prove existence, uniqueness and continuous-dependence results for the direct problem, uniqueness for the inverse problem and show how the stability can be restored in the inverse problem by a suitable a-priori bound.
Supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung (project S32/03)
Supported in part by a grant within the Cultural Exchange Treaty between Austria and Italy (project no. 55)
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© 1987 Springer Basel AG
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Engl, H.W., Langthaler, T., Manselli, P. (1987). On an Inverse Problem for a Nonlinear Heat Equation Connected with Continuous Casting of Steel. In: Hoffmann, KH., Krabs, W. (eds) Optimal Control of Partial Differential Equations II: Theory and Applications. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 78. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7627-8_5
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DOI: https://doi.org/10.1007/978-3-0348-7627-8_5
Publisher Name: Birkhäuser, Basel
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