2019
Том 71
№ 11

All Issues

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

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

Full text (.pdf)


Abstract

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).

English version (Springer): Ukrainian Mathematical Journal 52 (2000), no. 7, pp 1068-1074.

Citation Example: Khoma N. H., Khoma S. G., Mitropolskiy Yu. A. Smooth Solution of the Dirichlet Problem for a Quasilinear Hyperbolic Equation of the Second Order // Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 931-935.

Full text