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Zbl 1172.35458
Guezane-Lakoud, Assia; Chaoui, Abderrezak
A functional method applied to operator equations. (English)
[J] Banach J. Math. Anal. 3, No. 1, 52-60, electronic only (2009). ISSN 1735-8787/e

Summary: 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.

MSC 2000:: *35L90 Abstract hyperbolic evolution equations
35B45 A priori estimates
35D05 Existence of generalized solutions of PDE
35L10 Second order hyperbolic equations, general
35L20 Second order hyperbolic equations, boundary value problems

Keywords: unbounded operator's coefficients; strong generalized solution; energy integral method; Yosida approximation

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