On the~blow-up of the~solution of a~$(1+1)$-dimensional thermal--electrical model
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 2, pp. 249-262
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We consider a $(1+1)$-dimensional thermal–electrical model of semiconductor heating in an electric field. For the corresponding initial-boundary value problem, we prove the existence of a classical solution that cannot be continued in time and obtain sufficient conditions for the blow-up of the solution in a finite time.
Keywords:
nonlinear Sobolev-type equations, solution blow-up, local solvability, nonlinear capacity, blow-up time estimates.
@article{TMF_2024_219_2_a3,
author = {M. V. Artemeva and M. O. Korpusov},
title = {On the~blow-up of the~solution of a~$(1+1)$-dimensional thermal--electrical model},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {249--262},
publisher = {mathdoc},
volume = {219},
number = {2},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a3/}
}
TY - JOUR AU - M. V. Artemeva AU - M. O. Korpusov TI - On the~blow-up of the~solution of a~$(1+1)$-dimensional thermal--electrical model JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2024 SP - 249 EP - 262 VL - 219 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a3/ LA - ru ID - TMF_2024_219_2_a3 ER -
%0 Journal Article %A M. V. Artemeva %A M. O. Korpusov %T On the~blow-up of the~solution of a~$(1+1)$-dimensional thermal--electrical model %J Teoretičeskaâ i matematičeskaâ fizika %D 2024 %P 249-262 %V 219 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a3/ %G ru %F TMF_2024_219_2_a3
M. V. Artemeva; M. O. Korpusov. On the~blow-up of the~solution of a~$(1+1)$-dimensional thermal--electrical model. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 2, pp. 249-262. http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a3/