| Autor: |
Laister, Robert, Sierzega, Mikolaj |
| Rok vydání: |
2019 |
| Předmět: |
|
| Zdroj: |
Annales de l'Institut Henri Poincar\'e C, Analyse non lin\'eaire 37 (3), 2020, 709-725 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.anihpc.2019.12.001 |
| Popis: |
The problem of obtaining necessary and sufficient conditions for local existence of non-negative solutions in Lebesgue spaces for semilinear heat equations having monotonically increasing source term $f$ has only recently been resolved (Laister et al. (2016)). There, for the more difficult case of initial data in $L^1$, a necessary and sufficient integral condition on $f$ emerged. Here, subject to this integral condition, we consider other fundamental properties of solutions with $L^1$ initial data of indefinite sign, namely: uniqueness, regularity, continuous dependence and comparison. We also establish sufficient conditions for the global-in-time continuation of solutions for small initial data in $L^1$. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
