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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.
MSC:
35G16 Initial-boundary value problems for linear higher-order PDEs
80A05 Foundations of thermodynamics and heat transfer
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[1] Bland, DR, The Theory of Linear Viscoelasticity (1960), Oxford etc: Pergamon Press, Oxford etc
[2] Filimonov, AM; Kurchanov, PF; Myshkis, AD, Some unexpected results in the classical problem of vibration of the string with n beads when n is large, C. R. Acad. Sci., Paris, Sér. I, 313, 13, 961-965 (1991) · Zbl 0752.73044
[3] Filimonov, AM, Some unexpected results on the classical problem of vibrations of the string with N beads. The case of multiple frequencies, C. R. Acad. Sci., Paris, Sér. I, 315, 8, 957-961 (1992) · Zbl 0761.73053
[4] Filimonov, AM, Continuous approximations of difference operators, J. Difference Equ. Appl., 2, 4, 411-422 (1996) · Zbl 0882.34068
[5] Beckurts, KH; Wirtz, K., Neutron Physics (1964), Berlin etc: Springer, Berlin etc · Zbl 0129.22801
[6] Tzou, DY, Experimental support for the lagging behavior in heat propagation, J. Thermophys. Heat Transf., 9, 4, 686-693 (1995)
[7] Vlasov, V.; Rautian, NA, Properties of solutions of integro-differential equations arising in heat and mass transfer theory, Trans. Mosc. Math. Soc., 75, 2, 185-204 (2014) · Zbl 1318.47063
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