Geodesic
A Mixed Problem for a Class of Second-Order Nonlinear Hyperbolic Systems with Dirichlet and Poincar\'e Boundary Conditions
Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 702-720

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For a certain class of second-order hyperbolic systems, a mixed problem with Dirichlet and Poincaré boundary conditions is studied. In the linear case, an explicit representation of a soultion of this problem is given and questions related to its uniqueness and existence are studied depending on the character of nonlinearities in the system.
Keywords: semilinear hyperbolic system, mixed problem, a priori estimate
Mots-clés : Laplace invariants. 
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     author = {O. M. Dzhokhadze and S. S. Kharibegashvili and N. N. Shavlakadze},
     title = {A {Mixed} {Problem} for a {Class} of {Second-Order} {Nonlinear} {Hyperbolic} {Systems} with {Dirichlet} and {Poincar\'e} {Boundary} {Conditions}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_5_a4/}
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O. M. Dzhokhadze; S. S. Kharibegashvili; N. N. Shavlakadze. A Mixed Problem for a Class of Second-Order Nonlinear Hyperbolic Systems with Dirichlet and Poincar\'e Boundary Conditions. Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 702-720. http://geodesic.mathdoc.fr/item/MZM_2023_114_5_a4/