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. 1185–1209DOI 10.1016/J.ANIHPC.2020.04.002