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25 November 2001 Boundary value problems for second-order partial differential equations with operator coefficients
Kudratillo S. Fayazov, Eberhard Schock
Abstr. Appl. Anal. 6(5): 253-266 (25 November 2001). DOI: 10.1155/S1085337501000628

Abstract

Let ΩT be some bounded simply connected region in 2 with ΩT=Γ¯1Γ¯2. We seek a function u(x,t)((x,t)ΩT) with values in a Hilbert space H which satisfies the equation ALu(x,t)=Bu(x,t)+f(x,t,u,ut),(x,t)ΩT, where A(x,t),B(x,t) are families of linear operators (possibly unbounded) with everywhere dense domain D (D does not depend on (x,t)) in H and Lu(x,t)=utt+a11uxx+a1ut+a2ux. The values u(x,t);u(x,t)/n are given in Γ1. This problem is not in general well posed in the sense of Hadamard. We give theorems of uniqueness and stability of the solution of the above problem.

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Kudratillo S. Fayazov. Eberhard Schock. "Boundary value problems for second-order partial differential equations with operator coefficients." Abstr. Appl. Anal. 6 (5) 253 - 266, 25 November 2001. https://doi.org/10.1155/S1085337501000628

Information

Published: 25 November 2001
First available in Project Euclid: 13 April 2003

zbMATH: 1016.35001
MathSciNet: MR1879825
Digital Object Identifier: 10.1155/S1085337501000628

Subjects:
Primary: 35A07

Rights: Copyright © 2001 Hindawi

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Vol.6 • No. 5 • 25 November 2001
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