Geodesic
Solvability of the generalized Dirichlet problem for hyperbolic equations
Numerical methods and programming, Tome 3 (2002) no. 1, pp. 161-171.

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A priory inequalities with a negative norm are obtained for hyperbolic differential equations with Dirichlet boundary conditions for the case when the right-hand sides belong to a space of generalized functions. The existence and uniqueness of a generalized solution to the problem as well as the convergence of an approximate method are proved.
Keywords: generalized Dirichlet problem, hyperbolic equations, numerical methods, generalized functions. 
@article{VMP_2002_3_1_a12,
     author = {I. V. Kolos and M. V. Kolos},
     title = {Solvability of the generalized {Dirichlet} problem for hyperbolic equations},
     journal = {Numerical methods and programming},
     pages = {161--171},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2002_3_1_a12/}
}
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I. V. Kolos; M. V. Kolos. Solvability of the generalized Dirichlet problem for hyperbolic equations. Numerical methods and programming, Tome 3 (2002) no. 1, pp. 161-171. http://geodesic.mathdoc.fr/item/VMP_2002_3_1_a12/