REPRESENTATION OF SOLUTIONS TO THE NONLINEAR HEAT CONDUCTIVITY EQUATION BY TRIGONOMETRIC SERIES
https://doi.org/10.26583/vestnik.2024.330
EDN: ODCDWC
Abstract
The paper considers the nonlinear heat equation in a one-dimensional plane-symmetric case. For him, on the interval [0; p] the Cauchy problem with continuous initial data is posed. These data evenly continue to the segment [–p; 0], and then with a period of 2p on the entire numerical axis. The solution to the resulting Cauchy problem is represented in the form of a corresponding trigonometric series in cosines from the spatial variable. The coefficients of the series are the desired functions of time. For these coefficients, an infinite system of ordinary differential equations is given with the corresponding initial conditions. Finite segments of trigonometric sums are constructed that approximately convey the solutions of the considered Cauchy problems.
About the Authors
S. P. Bautin
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
I. A. Vazieva
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
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Review
For citations:
Bautin S.P., Vazieva I.A. REPRESENTATION OF SOLUTIONS TO THE NONLINEAR HEAT CONDUCTIVITY EQUATION BY TRIGONOMETRIC SERIES. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2024;13(3):154-159. (In Russ.) https://doi.org/10.26583/vestnik.2024.330. EDN: ODCDWC
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