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Higher-order degenerate Cauchy problems in locally convex spaces. (English) Zbl 1096.34035
Using the so-called \(C\)-propagation family of operators, the authors give conditions for the \(C\)-well-posedness of the higher-order degenerate Cauchy problem \[ \frac{d^n}{dt^n}Bu(t) = Au(t), t \geq 0, \;(Bu)^{(k)}(0)=Bu_k, 0 \leq k \leq n-1, \tag{1} \] where \(A\) and \(B\) are closed linear operators in a sequentially complete locally convex topological space. As an application, problem (1) with \(n=2\) and differential operators \(A\) and \(B\) is considered.

34G10 Linear differential equations in abstract spaces
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
Full Text: DOI
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