2019
Том 71
№ 11

All Issues

Khoma S. G.

Articles: 2
Article (Ukrainian)

Smooth Solution of the Dirichlet Problem for a Quasilinear Hyperbolic Equation of the Second Order

Khoma N. H., Khoma S. G., Mitropolskiy Yu. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 931-935

On the basis of the exact solution of the linear Dirichlet problem \(u_{tt} - u_{xx} = f\left( {x,t} \right)\) , \(u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0,{\text{ }}u\left( {x,0} \right) = u\left( {x,2\pi } \right) = 0,\) \(0 \leqslant x \leqslant \pi ,{\text{ }}0 \leqslant t \leqslant 2\pi ,\) we obtain conditions for the solvability of the corresponding Dirichlet problem for the quasilinear equation u ttu xx = f(x, t, u, u t).

Brief Communications (Ukrainian)

Solution of one boundary-value problem for a hyperbolic equation of the second order

Khoma S. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 4. - pp. 572-573

We find conditions for the existence of the classical solution of the boundary-value problem u tt -u xx = f(x,t), u(0,t)=u(π, t)=0, u(x, 0)=u(x, 2π).