抽象微分代数方程解的存在性及定性行为
Existence and qualitative behavior of solutions of abstract differential-algebraic equations
AI总结：
本文研究了半线性抽象微分代数方程解的存在性与定性行为，探讨了解的唯一性、最大存在区间、全局可解性、有界性及爆破现象。
摘要：
本文研究了一类半线性抽象微分代数方程（ADAEs）。给出了关于解的存在性与唯一性、解的最大存在区间、ADAEs的全局可解性、解的有界性以及解的爆破的定理。此前，通过投影将ADAEs转化为显式微分方程和代数方程组。该方程组的方程个数取决于ADAEs特征 pencil的索引。我们考虑了任意高索引的pencil。
英文摘要：
Abstract differential-algebraic equations (ADAEs) of a semilinear type are studied. Theorems on the existence and uniqueness of solutions and the maximal interval of existence, on the global solvability of the ADAEs, the boundedness of solutions and the blow-up of solutions are presented. Previously, an ADAE is reduced to a system of explicit differential equations and algebraic equations by using projectors. The number of equations of the system depends on the index of the characteristic pencil of the ADAE. We consider the pencil of an arbitrarily high index.
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