Blow-up of Solutions of the Cauchy Problem for the Doubly Nonlinear Equation of a Thermoelectric Model

M. V. Artemeva^a, M. O. Korpusov^ab, A. K. Matveeva<sup>a

a</sup> Lomonosov Moscow State University
^b Peoples' Friendship University of Russia named after Patrice Lumumba, Moscow

Abstract: A thermoelectric $(3+1)$-dimensional model of heating a dielectric in an electric field is considered which takes into account the Kerr nonlinear dependence of permittivity on the magnitude of field strength. For the corresponding Cauchy problem, the existence of a noncontinuable classical solution is proved and a result concerning the blow-up of a solution is obtained.

Keywords: nonlinear Sobolev-type equation, blow-up, local solvability, nonlinear capacity, estimates of blow-up time.

UDC: 517.538

Received: 12.10.2024

DOI: 10.4213/mzm14538

 English version: Mathematical Notes, 2025, 118:2, 215–221

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