Smooth Solution of the Dirichlet Problem for a Quasilinear Hyperbolic Equation of the Second Order - Mitropolskiy, Yu. A.; Khoma, N. H.; Khoma, S. G.; Митропольський, Ю. О.; Хома, H. Г.; Хома, С. Г. (Institute of Mathematics, NAS of Ukraine, 2000)
On the basis of the exact solution of the linear Dirichlet problem \(u_{tt} - u_{xx} = f\left( {x,t} \right)\) , \(u\left( {0,t} \right) = u\left( {π ,t} \right) = 0,{\text{ }}u\left( {x,0} \right) = u\left( {x,2π } \right) = 0,\) \(0 \leqslant x \leqslant π ,{\text{ }}0 \leqslant t \leqslant 2π ,\) we obtain conditions for the solvability of the corresponding Dirichlet problem for the quasilinear equation u tt − u xx = f(x, t, u, u t).