We study a nonclassical heat model with the time delay by using an approximate intermediate model presenting by a nonclassical linear partial differential equation with constant coefficients involving higher time-derivative of order m + 1 and the second order derivative with respect to the spatial variable in the one-dimensional case. We show that the trivial solution to the intermediate equation with homogeneous initial and boundary conditions is stable only if m = 1, i.e., in the case of the classical heat equation. Bibliography: 7 titles.
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Translated from Problemy Matematicheskogo Analiza 103, 2020, pp. 155-158.
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Kachalkin, I.O., Filimonov, A.M. Well-Posedness of Intermediate Models in Heat Problems. J Math Sci 249, 989–993 (2020). https://doi.org/10.1007/s10958-020-04990-z
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DOI: https://doi.org/10.1007/s10958-020-04990-z