Abstract
We study the boundary value problem for the quasilinear equation u u − uxx=F[u, ut], u(x, 0)= u(x, π)=0, u(x+w, t)=u(x, t), x ε ®, t ε [0, π], and establish conditions under which a theorem on the uniqueness of a smooth solution is true.
References
Yu. A. Mitropol’skii and N. H. Khoma, “Periodic solutions of quasilinear hyperbolie equations of second order,” Ukr. Mat. Zh., 47, No. 10, 1370–1375 (1995).
N. H. Khoma, “The existence of a smooth solution of a boundary-value problem,” Ukr. Mat. Zh., 47, No. 12, 1717–1719 (1995).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 12, pp. 1712–1716, December, 1997.
Rights and permissions
About this article
Cite this article
Khoma, N.H., Tsynalko, P.V. Smooth solution of one boundary-value problem. Ukr Math J 49, 1932–1937 (1997). https://doi.org/10.1007/BF02513073
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02513073