Geodesic
Classical solutions for a class of nonlinear wave equations
Theoretical and applied mechanics, Tome 48 (2021) no. 2, p. 257

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We study a class of initial value problems subject to nonlinear partial differential equations of hyperbolic type. A new topological approach is applied to prove the existence of nontrivial nonnegative solutions. More precisely, we propose a new integral representation of the solutions for the considered initial value problems and using this integral representation we establish existence of classical solutions for the considered classes of nonlinear wave equations.
DOI : 10.2298/TAM201123013G
Classification : 47H10, 58J20
Keywords: hyperbolic equations, nonnegative solution, fixed point, cone, sum of operators 
Svetlin Georgiev; Karima Mebarki; Khaled Zennir. Classical solutions for a class of nonlinear wave equations. Theoretical and applied mechanics, Tome 48 (2021) no. 2, p. 257 . doi: 10.2298/TAM201123013G
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     title = {Classical solutions for a class of nonlinear wave equations},
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     year = {2021},
     volume = {48},
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     doi = {10.2298/TAM201123013G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/TAM201123013G/}
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