Geodesic
On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model
Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 759-772.

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In this paper, we propose a system of nonlinear equations for the electric field potential and temperature, which describes the process of heating the semiconductor elements of an electrical board followed by thermal breakdown. For this system of equations, we prove the existence of a classical solution that is not extendable in time and also obtain sufficient conditions for the solution to blow up in finite time.
Keywords: electric field potential, first boundary value problem for the heat equation, Green's function, solution blow-up, methods of nonlinear capacity and test functions. 
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M. O. Korpusov; A. Yu. Perlov; A. V. Tymoshenko; R. S. Shafir. On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model. Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 759-772. http://geodesic.mathdoc.fr/item/MZM_2023_114_5_a8/

[1] A. V. Timoshenko, D. V. Kaleev, A. Yu. Perlov i dr., “Sravnitelnyi analiz analiticheskikh i empiricheskikh metodik otsenki tekuschikh parametrov nadezhnosti radiolokatsionnykh kompleksov monitoringa”, Izv. vysshikh uchebnykh zavedenii. Elektronika, 25:3 (2020), 244–254

[2] M. O. Korpusov, “O razrushenii resheniya uravneniya, rodstvennogo uravneniyu Gamiltona–Yakobi”, Matem. zametki, 93:1 (2013), 81–95 | DOI | MR | Zbl

[3] M. O. Korpusov, “O razrushenii resheniya nelokalnogo uravneniya s gradientnoi nelineinostyu”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 11, 43–53

[4] M. O. Korpusov, A. A. Panin, A. E. Shishkov, “O kriticheskom pokazatele “mgnovennoe razrushenie” versus “lokalnaya razreshimost” v zadache Koshi dlya modelnogo uravneniya sobolevskogo tipa”, Izv. RAN. Ser. matem., 85:1 (2021), 118–153 | DOI | MR

[5] F. G. Bass, V. S. Bochkov, Yu. S. Gurevich, Elektrony i fonony v ogranichennykh poluprovodnikakh, Nauka, M., 1984

[6] V. L. Bonch-Bruevich, S. G. Kalashnikov, Fizika poluprovodnikov, Nauka, M., 1990

[7] V. L. Bonch-Bruevich, I. P. Zvyagin, A. G. Mironov, Domennaya elektricheskaya neustoichivost v poluprovodnikakh, Nauka, M., 1972

[8] L. D. Landau, E. M. Lifshits, Elektrodinamika sploshnykh sred. Teoreticheskaya fizika, Nauka, M., 1992 | MR

[9] E. L. Mitidieri, S. I. Pokhozhaev, “Apriornye otsenki i otsutstvie reshenii nelineinykh uravnenii i neravenstv v chastnykh proizvodnykh”, Trudy MIAN, 234, Nauka, M., 2001, 3–383 | MR | Zbl

[10] V. A. Galaktionov, S. I. Pokhozhaev, “Uravneniya nelineinoi dispersii tretego poryadka: udarnye volny, volny razrezheniya i razrusheniya”, Zh. vychisl. matem. i matem. fiz., 48:10 (2008), 1819–1846 | MR | Zbl

[11] S. I. Pokhozhaev, “O razrushenii reshenii uravneniya Kuramoto–Sivashinskogo”, Matem. sb., 199:9 (2008), 97–106 | DOI | MR | Zbl

[12] A. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov, A. P. Mikhailov, Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii, Nauka, M., 1987

[13] G. A. Sviridyuk, “K obschei teorii polugrupp operatorov”, UMN, 49:4(298) (1994), 47–74 | MR | Zbl

[14] A. G. Sveshnikov, A. B. Alshin, M. O. Korpusov, Yu. D. Pletner, Lineinye i nelineinye uravneniya sobolevskogo tipa, FIZMATLIT, M., 2007

[15] N. V. Krylov, Lektsii po ellipticheskim i parabolicheskim uravneniyam v prostranstvakh Geldera, Nauchnaya kniga, Novosibirsk, 1998 | MR

[16] A. Fridman, Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968

[17] O. A. Ladyzhenskaya, V. A. Solonnikova, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967 | MR

[18] V. Pogozhelskii, “Issledovanie integralov parabolicheskogo uravneniya i kraevykh zadach v neogranichennoi oblasti”, Matem. sb., 47 (89):4 (1959), 397–430 | MR | Zbl

[19] A. A. Panin, “O lokalnoi razreshimosti i razrushenii resheniya abstraktnogo nelineinogo integralnogo uravneniya Volterra”, Matem. zametki, 97:6 (2015), 884–903 | DOI | MR

[20] G. N. Vatson, Teoriya besselevykh funktsii. Chast I, IL, M., 1949 | MR