تقرير
On regularity of mild solutions for autonomous linear retarded functional differential equations
| العنوان: | On regularity of mild solutions for autonomous linear retarded functional differential equations |
|---|---|
| المؤلفون: | Nishiguchi, Junya |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, Primary 34K05, 34K06, Secondary 34K99, 26A42 |
| الوصف: | The notion of mild solutions for autonomous linear retarded functional differential equations (RFDEs) has been introduced in [J. Nishiguchi, Electron.\ J. Qual.\ Theory Differ.\ Equ.\ \textbf{2023}, No.~32, 1--77] for the purpose of defining fundamental matrix solutions and obtaining a variation of constants formula for the RFDEs. This notion gives a straightforward definition of solutions to the RFDEs under discontinuous history functions compared with previous studies in the literature. For a given autonomous linear RFDE, it holds that the fundamental matrix solutions are locally Lipschitz continuous on the interval $[0, \infty)$. However, it is not apparent whether a similar property is true for the mild solutions. Here we obtain a result which shows the regularity of mild solutions on $[0, \infty)$ for autonomous linear RFDEs. The result makes clear a connection between the mild solutions and solution concepts in previous studies. Comment: 16 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.11777 |
| رقم الأكسشن: | edsarx.2407.11777 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |