Existence of solutions for a higher-order semilinear parabolic equation with singular initial data

Ishige, Kazuhiro; Kawakami, Tatsuki; Okabe, Shinya

doi:10.1016/j.anihpc.2020.04.002

Ishige, Kazuhiro ¹ ; Kawakami, Tatsuki ² ; Okabe, Shinya ³

¹ Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
² Applied Mathematics and Informatics Course, Faculty of Advanced Science and Technology, Ryukoku University, 1-5 Yokotani, Seta Oe-cho, Otsu, Shiga 520-2194, Japan
³ Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan

Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 5, pp. 1185-1209.

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Résumé

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.

MR Zbl

DOI : 10.1016/j.anihpc.2020.04.002

Mots-clés : Higher-order semilinear parabolic equation, Majorizing kernel, Singular initial data, Solvability

Affiliations des auteurs :

Ishige, Kazuhiro ¹ ; Kawakami, Tatsuki ² ; Okabe, Shinya ³

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     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 = {https://www.numdam.org/articles/10.1016/j.anihpc.2020.04.002/}
}

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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. https://www.numdam.org/articles/10.1016/j.anihpc.2020.04.002/

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