References
Haraux, A., Zuazua, E.: Decay estimates for some semilinear damped hyperbolic problems. Arch. Ration. Mech. Anal.100, 191–206 (1987)
Lions, J.L.: Quelque Méthodes de Resolution de Problèmes aux Limites Non-Linèares. Paris: Dunod Gautier Villars 1969
Nakao, M.: Asymptotic stability of the bounded or almost periodic solution of the wave equation with nonlinear dissipative term. J. Math. Anal. Appl.58, 336–343 (1977)
Nakao, M.: Periodic solution and decay for some nonlinear wave equations with sublinear dissipative terms. Nonlinear Anal. Theory. Methods Appl.10, 587–602 (1986)
Nakao, M.: On the decay of solutions of some nonlinear dissipative wave equations in higher dimensions. Math. Z.193, 227–234 (1986)
Nakao, M.: On solutions of the wave equation with a sublinear dissipative term. J. Differ. Equations69, 204–215 (1987)
Nakao, M.: Existence of global classical solutions of the initial-boundary value problem for some nonlinear wave equations. J. Math. Anal. Appl.146, 217–240 (1990)
Nakao, M.: On solutions of the wave equation with a sublinear dissipative term II. Funkc. Ekvacioj, Ser. Int.33, 307–316 (1990)
Shibata, Y.: On the global existence of classical solutions of mixed problem for some second order nonlinear hyperbolic operators with dissipative term in the interior domain. Funkc. Ekvacioj, Ser. Int.25, 303–345 (1982)
Strauss, W.: Energy Methods in Nonlinear Partial Differential Equations. Notas de Matematics, Rio de Janeiro: 1969
Zuazua, E.: Stability and decay for a class of nonlinear hyperbolic problems. Asymptotic Anal.1, 161–185 (1988)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nakao, M. Remarks on the existence and uniqueness of global decaying solutions of the nonlinear dissipative wave equations. Math Z 206, 265–276 (1991). https://doi.org/10.1007/BF02571342
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02571342