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.
Original language | English |
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Pages (from-to) | 1185-1209 |
Number of pages | 25 |
Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
Volume | 37 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2020 Sep 1 |
Externally published | Yes |
Keywords
- Higher-order semilinear parabolic equation
- Majorizing kernel
- Singular initial data
- Solvability
ASJC Scopus subject areas
- Analysis
- Mathematical Physics
- Applied Mathematics