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Approximate analytic solution of heat conduction problems with a mismatch between initial and boundary conditions. (English. Russian original) Zbl 1197.35291

Russ. Math. 54, No. 4, 55-61 (2010); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2010, No. 4, 63-71 (2010).
Summary: We consider a heat conduction problem for an infinite plate with a mismatch between initial and boundary conditions. Using the method of integral relations, we obtain an approximate analytic solution to this problem by determining the temperature perturbation front. The solution has a simple form of an algebraic polynomial without special functions. It allows us to determine the temperature state of the plate in the full range of the Fourier numbers (\(0\leq \, \text{{\textsf{F}}} \, <\infty \)) and is especially effective for very small time intervals.

MSC:

35Q79 PDEs in connection with classical thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
35C11 Polynomial solutions to PDEs
35A35 Theoretical approximation in context of PDEs
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References:

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