2019
Том 71
№ 4

All Issues

Tsynalko P. V.

Articles: 3
Article (Ukrainian)

On a smooth solution of a boundary-value problem

Tsynalko P. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 9. - pp. 1293–1296

We study a periodic boundary-value problem for the quasilinear equation u tt u xx =F[u, u t , u x ], u(x, 0)=u(x, π)=0, u(x + ω, t) = u(x, t), x ∈ ℝ t ∈ [0, π], and establish conditions that guarantee the validity of a theorem on unique solvability.

Brief Communications (Ukrainian)

Smooth solution of one boundary-value problem

Khoma N. H., Tsynalko P. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1712–1716

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.

Article (Ukrainian)

A periodic problem for the inhomogeneous equation of string oscillations

Khoma G. P., Mitropolskiy Yu. A., Tsynalko P. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 558–565

We study a periodic problem for the equation u tt−uxx=g(x, t), u(x, t+T)=u(x, t), u(x+ω, t)= =u(x, t), ℝ2 and establish conditions of the existence and uniqueness of the classical solution.