Investigation of the model for the essentially loaded heat equation
DOI:
https://doi.org/10.31489/2019No1/113-120Keywords:
thermophysical processes, electric arc, loaded heat equation, boundary value problem, reduction to integral equationAbstract
The studied problem for the essentially loaded heat equation is connected with mathematical modeling of thermophysical processes in the electric arc of high-current disconnecting devices. Experimental studies of such phenomena are difficult due to their transience, and in some cases only a mathematical model is able to provide adequate information about their dynamics. The study of the mathematical model is carried out when the order of the derivative in the loaded summand is less than, equal to and greater than the order of the differential part of the heat equation, at a fixed point of the load and in the case when the load point moves at a variable speed. The article is focused mainly on scientific researchers engaged in practical applications of loaded differential equations.
References
"1 Dzhenaliev M.T., Ramazanov M.I. Loaded equations as perturbations of differential equations. Almaty, Publishing house «Gylym», 2010, 334 p.
Kostetskaya G.S., Radchenko T.N. Metody matematicheskoy fiziki. Uravnenie teploprovodnosti [Methods of mathematical physics. Equation of heat conductivity]. Rostov-on-Don, Electronic textbook, 2016, 47 p. [in Russian]
Polyanin A.D. Spravochnik po lineynym uravneniyam matematicheskoy fiziki [Handbook of linear equations of mathematical physics]. Moscow, Fizmatlit Publ., 2001, 576 p. [in Russian]
Yesbayev A.N., Yessenbayeva G.A. On the properties of the kernel and the solvability of one integral equation of Volterra. Bulletin of Karaganda University. Mathematics Series. 2013, No. 2(70), pp. 65 – 69.
Prudnikov A.P., Brychkov Yu.A., Marychev O.I. Integrals and series: in Vol. 2. Special functions, Moscow: Fizmatlit, 2003, 664 p.
Yesbayev A.N., Yessenbayeva G.A. On the boundary value problem for a loaded differential heat conduction operator with the stationary point of load. Bulletin of Karaganda University. Mathematics Series. 2013, No. 2(70), pp. 59 – 65.
Polyanin A.D., Manzhirov A.V. Spravochnik po integral'nym uravneniyam: Metody resheniya [Handbook of Integral Equations: Solution Methods]. Moscow, Publishing House “Factorial Press», 2000, 384 p. [in Russian]
"
