It has been shown that inverse initial value problems are usually ill-posed, and unstable. In the present paper it is discussed that inverse problems of certain initial value problems which are unstable or chaotic in nature, can be well-posed, which indicates that their solutions are strable and can result in super-resolution. To demonstrate the possibility of well-posedness and super-resolution of the inverse initial value problems, numerical simulations of inverse anayses were made for differential equations describing chaotic phenomena. It was shown that under certain conditions very small variations in initial values can be estimated with good accuracy using the observations made later. The possibility of the super-resolution in the inverse analyses were indicated. The condition for the well-posedness of the inverse initial value problems was discussed.
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