Banach Journal of Mathematical Analysis

A functional method applied to operator equations

Abderrezak Chaoui and Assia Guezane-Lakoud

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Abstract

We consider second order hyperbolic equations with unbounded operator's coefficients possessing time dependent domain of definition in a Hilbert space. Existence and uniqueness of the strong generalized solution are studied. The proofs rely on a generalization of the well known energy integral method. First, we derive a priori estimates for the strong generalized solutions with the help of Yosida operator approximation. Then, using previous results, we show that the range of the operators generated by the posed problem is dense.

Article information

Source
Banach J. Math. Anal., Volume 3, Number 1 (2009), 52-60.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336423

Digital Object Identifier
doi:10.15352/bjma/1240336423

Mathematical Reviews number (MathSciNet)
MR2461746

Zentralblatt MATH identifier
1172.35458

Subjects
Primary: 35B45: A priori estimates
Secondary: 35D05 35L90: Abstract hyperbolic equations 35L10: Second-order hyperbolic equations 35L20: Initial-boundary value problems for second-order hyperbolic equations

Keywords
evolution equation a priori estimate strong generalized solution hyperbolic equation boundary value problem

Citation

Guezane-Lakoud, Assia; Chaoui, Abderrezak. A functional method applied to operator equations. Banach J. Math. Anal. 3 (2009), no. 1, 52--60. doi:10.15352/bjma/1240336423. https://projecteuclid.org/euclid.bjma/1240336423


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