## 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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