The final value problem for Sobolev equations-Reference-Cited by-同舟云学术

The final value problem for Sobolev equations

Published:1976 Issue:1 Volume:56 Page:247-252
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Lagnese John

Abstract

Let A A and B B be m m -accretive linear operators in a complex Hilbert space H H with D ( A ) ⊂ D ( B ) D(A) \subset D(B) . The method of quasi-reversibility is used to obtain a solution to the Sobolev equation ( d / d t ) [ ( I + B ) u ( t ) ] + A u ( t ) = 0 , 0 > t > 1 (d/dt)[(I + B)u(t)] + Au(t) = 0,0 > t > 1 , which approximates a specified final value u ( 1 ) = f u(1) = f . In general, when D ( A ) ⊂ D ( B ) D(A) \subset D(B) , it is not possible to find a solution which achieves exactly the final value u ( 1 ) = f u(1) = f .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1976-056-01/S0002-9939-1976-0419971-9/S0002-9939-1976-0419971-9.pdf

Reference7 articles.

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4. 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.

5. Equations with operators forming a right angle;Showalter, R. E.;Pacific J. Math.,1973

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