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Stability of semilinear ill-posed problems with a prescribed energy bound (1995)

Lyashenko, A. A.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 18 (1995), S. 549-569

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ISSN: 0170-4214

Keywords: Mathematics and Statistics ; Applied Mathematics

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: In the present paper we discuss the stability of semilinear problems of the form Aαu + Gα(u) = ƒ under assumption of an a priori bound for an energy functional Eα(u) ≤ E, where α is a parameter in a metric space M. Following [11] the problem Aαu + Gα(u) = ƒ, Eα(u) ≤ E is called stable in a Hilbert space H at a point α ∊ M if for any ƒ∊H, E, ∊ 〉 0 there exists δ 〉 0 such that for any functions uα1, uα2 satisfying Aαjuαj + Gαj(uαj) = ƒαj, Eαj(uαj) ≤ E, j = 1,2 we have ‖uα1 - uα2H ≤ ∊ provided ρM(αj, α) ≤ δ, ‖ƒαj - ƒ‖H ≤ δ, j = 1,2. In the present paper we obtain stability conditions for the problem Aαu + Gα(u) = ƒ, Eα(u) ≤ E.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/mma.1670180705

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