Messaoudi, Salim A.Bouhoufani, OuliaIlhem, HamchiAlahyane, Mohamed2022-10-312022-10-312021-11-16Messaoudi, S. A., Bouhoufani, O., Hamchi, I., & Alahyane, M. (2021). Existence and blow up in a system of wave equations with nonstandard nonlinearities. <i>Electronic Journal of Differential Equations, 2021</i>(91), pp. 1-33.1072-6691https://hdl.handle.net/10877/16273In this article, we consider a coupled system of two nonlinear hyperbolic equations, where the exponents in the damping and source terms are variables. First, we prove a theorem of existence and uniqueness of weak solution, by using the Faedo Galerkin approximations and the Banach fixed point theorem. Then, using the energy method, we show that certain solutions with positive initial energy blow up in finite time. We also give some numerical applications to illustrate our theoretical results.Text33 pages1 file (.pdf)enAttribution 4.0 InternationalHyperbolic systemExistenceBlow upVariable exponentsNonlinearArticle