On the~blowup of solutions of the~Cauchy problem for nonlinear equations of ferroelectricity theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 3, pp. 327-339
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We study two Cauchy problems for nonlinear equations of the Sobolev type, of the form $ \frac{\partial}{\partial t}\frac{\partial^2u}{\partial x_3^2} + \Delta u=|u|^q $ and $ \frac{\partial}{\partial t}\Delta_{\perp}u + \Delta u= |u|^q$. We find conditions under which weak generalized local-in-time solutions of the Cauchy problem exist, and we also find conditions under which solutions blow up.
Keywords:
Sobolev-type nonlinear equations, blowup, local solvability, nonlinear capacity.
@article{TMF_2022_212_3_a0,
author = {M. O. Korpusov and R. S. Shafir},
title = {On the~blowup of solutions of {the~Cauchy} problem for nonlinear equations of ferroelectricity theory},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {327--339},
publisher = {mathdoc},
volume = {212},
number = {3},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2022_212_3_a0/}
}
TY - JOUR AU - M. O. Korpusov AU - R. S. Shafir TI - On the~blowup of solutions of the~Cauchy problem for nonlinear equations of ferroelectricity theory JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2022 SP - 327 EP - 339 VL - 212 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2022_212_3_a0/ LA - ru ID - TMF_2022_212_3_a0 ER -
%0 Journal Article %A M. O. Korpusov %A R. S. Shafir %T On the~blowup of solutions of the~Cauchy problem for nonlinear equations of ferroelectricity theory %J Teoretičeskaâ i matematičeskaâ fizika %D 2022 %P 327-339 %V 212 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2022_212_3_a0/ %G ru %F TMF_2022_212_3_a0
M. O. Korpusov; R. S. Shafir. On the~blowup of solutions of the~Cauchy problem for nonlinear equations of ferroelectricity theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 3, pp. 327-339. http://geodesic.mathdoc.fr/item/TMF_2022_212_3_a0/