PageHeader : Funkcialaj Ekvacioj, 25 (1982) 303-345 Title : On the Global Existence of Classical Solutions of Mixed Problem Title : for Some Second Order Non-linear Hyperbolic Operators Title : with Dissipative Term in the Interior Domain AuthorInfo : By AuthorInfo : Yoshihiro SHIBATA AuthorInfo : (University of Tsukuba, Japan) section : 1. Introduction. section : 2. Preliminaries. subsection : 2.1. Notations. subsection : 2.2. Interpolation inequalities. subsection : 2.3. Compatibility condition. subsection : 2.4. The ``smoothing'' operator. section : 3. Iteration scheme. section : 4. Decay estimates for the linearized problem. section : 5. Proofs of main theorems. section : References