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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.

##### MSC:
 34G10 Linear differential equations in abstract spaces 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
##### Keywords:
degenerate Cauchy problem; well-posedness
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##### References:
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