The final value problem for Sobolev equations

Lagnese, John

doi:10.1090/S0002-9939-1976-0419971-9

The final value problem for Sobolev equations
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by John Lagnese

Proc. Amer. Math. Soc. 56 (1976), 247-252

DOI: https://doi.org/10.1090/S0002-9939-1976-0419971-9

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Erratum: Proc. Amer. Math. Soc. 63 (1977), 375.

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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