About heat wave in a semi-infinite rod with a boundary condition periodically changing in time. (English. Russian original) Zbl 1536.35169
J. Math. Sci., New York 277, No. 4, 619-627 (2023); translation from Zap. Nauchn. Semin. POMI 493, 218-231 (2020).
Summary: An exact analytical solution to the problem of a periodic heat wave in a semi-infinite rod with a time-varying boundary condition at its end has been obtained and investigated. The 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.
MSC:
| 35K05 | Heat equation |
| 35C05 | Solutions to PDEs in closed form |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
References:
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