Existence of solutions for a higher-order semilinear parabolic equation with singular initial data
Analysis of PDEs
2019-09-13 v1
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.
Keywords
Cite
@article{arxiv.1909.05492,
title = {Existence of solutions for a higher-order semilinear parabolic equation with singular initial data},
author = {Kazuhiro Ishige and Tatsuki Kawakami and Shinya Okabe},
journal= {arXiv preprint arXiv:1909.05492},
year = {2019}
}