In this paper, we consider the boundary value problem related to the quasilinear hyperbolic equation with nonlinear source terms. We start by showing the local existence theorem. Then, we prove the global existence and the decay of the energy by using Nakao's inequality, finally we get the finite time blow up of solutions.
Bounaama, A., Maouni, M. & Ouaoua, A. (2023). Global existence, decay and blow up of solutions for a quasilinear hyperbolic equations with source terms. International Journal of Nonlinear Analysis and Applications, 14(1), 1977–1988. https://doi.org/10.22075/ijnaa.2022.27362.3574
MLA
Bounaama, A., Maouni, M., & Ouaoua, A. "Global existence, decay and blow up of solutions for a quasilinear hyperbolic equations with source terms", International Journal of Nonlinear Analysis and Applications, 14, 1, 2023, 1977–1988. doi: 10.22075/ijnaa.2022.27362.3574
HARVARD
Bounaama, A., Maouni, M., & Ouaoua, A. (2023). 'Global existence, decay and blow up of solutions for a quasilinear hyperbolic equations with source terms', International Journal of Nonlinear Analysis and Applications, 14(1), pp. 1977–1988. doi: 10.22075/ijnaa.2022.27362.3574
CHICAGO
Bounaama, A., Maouni, M. & Ouaoua, A., "Global existence, decay and blow up of solutions for a quasilinear hyperbolic equations with source terms." International Journal of Nonlinear Analysis and Applications, 14 1 (2023): 1977–1988, doi: 10.22075/ijnaa.2022.27362.3574
VANCOUVER
Bounaama A., Maouni M., Ouaoua A. Global existence, decay and blow up of solutions for a quasilinear hyperbolic equations with source terms. IJNAA. 2023;14(1):1977–1988. doi: 10.22075/ijnaa.2022.27362.3574
International Journal of Nonlinear Analysis and Applications