Abstract
We consider two space-periodic transmission problems for the heat equation. By means of space-periodic layer heat potentials, we convert the problems into systems of integral equations. Then we establish the invertibility of the operators appearing in the integral equations and we deduce the unique solvability in parabolic Schauder spaces of the transmission problems.
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Acknowledgements
The authors acknowledge the support of the project BIRD168373/16 ‘Singular perturbation problems for the heat equation in a perforated domain’ of the University of Padova. The authors are members of the ‘Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni’ (GNAMPA) of the ‘Istituto Nazionale di Alta Matematica’ (INdAM).
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Luzzini, P., Musolino, P. (2019). Periodic Transmission Problems for the Heat Equation. In: Constanda, C., Harris, P. (eds) Integral Methods in Science and Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-16077-7_17
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DOI: https://doi.org/10.1007/978-3-030-16077-7_17
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