Abstract
We prove an existence and uniqueness result for an inverse problem arising from a phase-field model with two memory kernels. More precisely, we identify the convolution memory kernels and the diffusion coefficient besides the temperature and the phase-field parameter. We prove our results in the framework of Sobolev spaces. Our fundamental tools are an optimal regularity result in the Lp spaces and fixed point arguments.
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Colombo, F., Guidetti, D. (2005). An Inverse Problem for a Phase-field Model in Sobolev Spaces. In: Brezis, H., Chipot, M., Escher, J. (eds) Nonlinear Elliptic and Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 64. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7385-7_10
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DOI: https://doi.org/10.1007/3-7643-7385-7_10
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7266-8
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