English

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}
}