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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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

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

First available in Project Euclid: 13 April 2003

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Primary: 35A07


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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