Abstract and Applied Analysis

Boundary value problems for second-order partial differential equations with operator coefficients

Kudratillo S. Fayazov and Eberhard Schock

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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.

Article information

Source
Abstr. Appl. Anal., Volume 6, Number 5 (2001), 253-266.

Dates
First available in Project Euclid: 13 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1050266864

Digital Object Identifier
doi:10.1155/S1085337501000628

Mathematical Reviews number (MathSciNet)
MR1879825

Zentralblatt MATH identifier
1016.35001

Subjects
Primary: 35A07

Citation

Fayazov, Kudratillo S.; Schock, Eberhard. Boundary value problems for second-order partial differential equations with operator coefficients. Abstr. Appl. Anal. 6 (2001), no. 5, 253--266. doi:10.1155/S1085337501000628. https://projecteuclid.org/euclid.aaa/1050266864


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