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Well-posedness of intermediate models in heat problems. (English. Russian original) Zbl 1448.35105
J. Math. Sci., New York 249, No. 6, 989-993 (2020); translation from Probl. Mat. Anal. 103, 155-158 (2020).
Summary: 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.
35G16 Initial-boundary value problems for linear higher-order PDEs
80A05 Foundations of thermodynamics and heat transfer
Full Text: DOI
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