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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The final value problem for Sobolev equations
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by John Lagnese PDF
Proc. Amer. Math. Soc. 56 (1976), 247-252 Request permission

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 $u(1) = f$.
References
    N. Dunford and J. T. Schwartz, Linear operators. II: Spectral theory. Selfadjoint operators in Hilbert space, Wiley, New York, 1963. MR 32 #6181.
  • Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • John Lagnese, Existence, uniqueness and limiting behavior of solutions of a class of differential equations in Banach space, Pacific J. Math. 53 (1974), 473–485. MR 361336
  • R. Lattés and J.-L. Lions, The method of quasi-reversibility, Modern Analytic and Computational Methods in Sci. and Math., no. 18, Elsevier, New York, 1969. MR 39 #5067.
  • R. E. Showalter, Equations with operators forming a right angle, Pacific J. Math. 45 (1973), 357–362. MR 318971
  • R. E. Showalter, The final value problem for evolution equations, J. Math. Anal. Appl. 47 (1974), 563–572. MR 352644, DOI 10.1016/0022-247X(74)90008-0
  • Kôsaku Yosida, Functional analysis, Die Grundlehren der mathematischen Wissenschaften, Band 123, Academic Press, Inc., New York; Springer-Verlag, Berlin, 1965. MR 0180824
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 247-252
  • MSC: Primary 34G05; Secondary 35R20
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0419971-9
  • MathSciNet review: 0419971