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The Final Value Problem for Sobolev Equations
1976
Proceedings of the American Mathematical Society
Let A and B be m-accretive linear operators in a complex Hubert space H with D{A) C 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 < l < 1, which approximates a specified final value u(\) = f. In general, when D(A) C D(B), it is not possible to find a solution which achieves exactly the final value w(l) = /.
doi:10.2307/2041612
fatcat:ur25pgn2frh7hbzmubhdlumg2a