Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 3, Number 1 (2009), 52-60.
A functional method applied to operator equations
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.
Banach J. Math. Anal., Volume 3, Number 1 (2009), 52-60.
First available in Project Euclid: 21 April 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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