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Second order equations in functional spaces: qualitative and discrete well-posedness. (English) Zbl 1433.34081

Summary: The present survey contains the recent results on the local and nonlocal well-posed problems for second order differential and difference equations. Results on the stability of differential problems for second order equations and of difference schemes for approximate solution of the second order problems are presented.

MSC:

34G10 Linear differential equations in abstract spaces
34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
65L12 Finite difference and finite volume methods for ordinary differential equations
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References:

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