JournalsaihpcVol. 37, No. 5pp. 1185–1209

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

  • Shinya Okabe

    Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan

  • Kazuhiro Ishige

    Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

  • Tatsuki Kawakami

    Applied Mathematics and Informatics Course, Faculty of Advanced Science and Technology, Ryukoku University, 1-5 Yokotani, Seta Oe-cho, Otsu, Shiga 520-2194, Japan
Existence of solutions for a higher-order semilinear parabolic equation with singular initial data cover

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Abstract

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.

Cite this article

Shinya Okabe, Kazuhiro Ishige, Tatsuki Kawakami, Existence of solutions for a higher-order semilinear parabolic equation with singular initial data. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 5, pp. 1185–1209

DOI 10.1016/J.ANIHPC.2020.04.002