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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     author = {M. O. Korpusov and A. Yu. Perlov and A. V. Tymoshenko and R. S. Shafir},
     title = {On the {Blow-Up} of the {Solution} of a {Nonlinear} {System} of {Equations} of a {Thermal-Electrical} {Model}},
     journal = {Matemati\v{c}eskie zametki},
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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/