Criterion of the global solvability of regular and singular differential-algebraic equations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915095252041728 |
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| author | Filipkovska, Maria |
| author_facet | Filipkovska, Maria |
| contents | For regular and nonregular (singular) semilinear differential-algebraic equations (DAEs), we prove theorems on the existence and uniqueness of global solutions and on the blow-up of solutions, which allow one to identify the sets of initial values for which the initial value problem has global solutions and/or for which solutions is blow-up in finite time, as well as the regions that the solutions cannot leave. Together these theorems provide a criterion of the global solvability of semilinear DAEs. As a consequence, we obtain conditions for the global boundedness of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Criterion of the global solvability of regular and singular differential-algebraic equations Filipkovska, Maria Classical Analysis and ODEs 34A09, 34A12, 15A22, 34C11, 34D23 For regular and nonregular (singular) semilinear differential-algebraic equations (DAEs), we prove theorems on the existence and uniqueness of global solutions and on the blow-up of solutions, which allow one to identify the sets of initial values for which the initial value problem has global solutions and/or for which solutions is blow-up in finite time, as well as the regions that the solutions cannot leave. Together these theorems provide a criterion of the global solvability of semilinear DAEs. As a consequence, we obtain conditions for the global boundedness of solutions. |
| title | Criterion of the global solvability of regular and singular differential-algebraic equations |
| topic | Classical Analysis and ODEs 34A09, 34A12, 15A22, 34C11, 34D23 |
| url | https://arxiv.org/abs/2401.07354 |