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We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.
Ishige, Kazuhiro 1 ; Kawakami, Tatsuki 2 ; Okabe, Shinya 3
@article{AIHPC_2020__37_5_1185_0,
author = {Ishige, Kazuhiro and Kawakami, Tatsuki and Okabe, Shinya},
title = {Existence of solutions for a higher-order semilinear parabolic equation with singular initial data},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1185--1209},
publisher = {Elsevier},
volume = {37},
number = {5},
year = {2020},
doi = {10.1016/j.anihpc.2020.04.002},
mrnumber = {4138231},
zbl = {1454.35222},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.04.002/}
}
TY - JOUR AU - Ishige, Kazuhiro AU - Kawakami, Tatsuki AU - Okabe, Shinya TI - Existence of solutions for a higher-order semilinear parabolic equation with singular initial data JO - Annales de l'I.H.P. Analyse non linéaire PY - 2020 SP - 1185 EP - 1209 VL - 37 IS - 5 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.04.002/ DO - 10.1016/j.anihpc.2020.04.002 LA - en ID - AIHPC_2020__37_5_1185_0 ER -
%0 Journal Article %A Ishige, Kazuhiro %A Kawakami, Tatsuki %A Okabe, Shinya %T Existence of solutions for a higher-order semilinear parabolic equation with singular initial data %J Annales de l'I.H.P. Analyse non linéaire %D 2020 %P 1185-1209 %V 37 %N 5 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.04.002/ %R 10.1016/j.anihpc.2020.04.002 %G en %F AIHPC_2020__37_5_1185_0
Ishige, Kazuhiro; Kawakami, Tatsuki; Okabe, Shinya. Existence of solutions for a higher-order semilinear parabolic equation with singular initial data. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 5, pp. 1185-1209. doi : 10.1016/j.anihpc.2020.04.002. http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.04.002/
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