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Proceedings of the American Mathematical Society

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The final value problem for Sobolev equations

Author: John Lagnese
Journal: Proc. Amer. Math. Soc. 56 (1976), 247-252
MSC: Primary 34G05; Secondary 35R20
Erratum: Proc. Amer. Math. Soc. 63 (1977), 375.
MathSciNet review: 0419971
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Abstract: Let $ A$ and $ B$ be $ m$-accretive linear operators in a complex Hilbert space $ H$ with $ D(A) \subset D(B)$. The method of quasi-reversibility is used to obtain a solution to the Sobolev equation $ (d/dt)[(I + B)u(t)] + Au(t) = 0,0 < t < 1$, which approximates a specified final value $ u(1) = f$. In general, when $ D(A) \subset D(B)$, it is not possible to find a solution which achieves exactly the final value $ u(1) = f$.

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Article copyright: © Copyright 1976 American Mathematical Society