Smooth Solution of the Dirichlet Problem for a Quasilinear Hyperbolic Equation of the Second Order
On the basis of the exact solution of the linear Dirichlet problem \(u_tt - u_xx = f( x,t )\) , \(u( 0,t ) = u( π ,t ) = 0, u( x,0 ) = u( x,2π ) = 0,\) \(0 x π , 0 t 2π ,\) 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)., number=7, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Mitropolskiy, Yu. A. and Khoma, N. H. and Khoma, S. G., year=2000, month=Jul., pages=931–935