On a smooth solution of a nonlinear periodic boundary-value problem
- 12 Downloads
We establish conditions for the existence of a smooth solution of a quasilinear hyperbolic equationu tt - uxx = ƒ(x, t, u, u, u x),u (0,t) = u (π,t) = 0,u (x, t+ T) = u (x, t), (x, t) ∈ [0, π] ×R, and prove a theorem on the existence and uniqueness of a solution.
KeywordsBanach Space Wave Equation Periodic Solution Integral Representation Russian Translation
Unable to display preview. Download preview PDF.
- 1.Yu. A. Mitropol’skii, G. P. Khoma, and M. I. Gromyak,Asymptotic Methods for Investigation of Quasiwave Hyperbolic Equations [in Russian], Naukova Dumka, Kiev (1991).Google Scholar
- 3.O. Vejvoda and M. Štedry, “Existence of classical periodic solutions for wave equations: the relationship between the number-theoretical character of the period and the geometrical properties of solutions,”Differents. Uravn.,20, No. 10, 1733–1739 (1984).Google Scholar