2019
Том 71
№ 11

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

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.

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