Geodesic
About heat wave in a semi-infinite rod with a boundary condition periodically changing in time
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 218-231

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It has been obtained and investigated an exact analytical solution of the problem of a periodic heat wave in a semi-infinite rod with a time-varying boundary condition at its end. Тhe end of the rod is maintained at a given temperature (inhomogeneous Dirichlet condition) during the first half of the time period, the end of the rod is heat insulated (homogeneous Neumann condition) in the second half of the time period. The problem is solved by the Wiener-Hopf method. Numerical calculations of temperature distribution are given for temperature wave. 
@article{ZNSL_2020_493_a14,
     author = {V. D. Lukyanov},
     title = {About heat wave in a semi-infinite rod with a boundary condition periodically changing in time},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {218--231},
     publisher = {mathdoc},
     volume = {493},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a14/}
}
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V. D. Lukyanov. About heat wave in a semi-infinite rod with a boundary condition periodically changing in time. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 218-231. http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a14/