Solvability of the Solution of Superlinear Hyperbolic Dirichlet Problem
Main Article Content
Abstract
In this paper, we aim to study the solutions of superlinear hyperbolic problems with boundary condition of Dirichlet type where we show the existence and the uniqueness of the strong solutions for the superlinear problems by the method of energy inequality.
Article Details
References
- G. Bahia, A. Ouannas, I.M. Batiha, Z. Odibat, The Optimal Homotopy Analysis Method Applied on Nonlinear Timefractional Hyperbolic Partial Differential Equations, Numer. Methods Partial Differ. Equ. 37 (2020), 2008–2022. https://doi.org/10.1002/num.22639.
- T.E. Oussaeif, B. Antara, A. Ouannas, et al. Existence and Uniqueness of the Solution for an Inverse Problem of a Fractional Diffusion Equation with Integral Condition, J. Funct. Spaces. 2022 (2022), 7667370. https://doi.org/10.1155/2022/7667370.
- Z. Chebana, T.E. Oussaeif, A. Ouannas, I. Batiha, Solvability of Dirichlet Problem for a Fractional Partial Differential Equation by Using Energy Inequality and Faedo-Galerkin Method, Innov. J. Math. 1 (2022), 34–44. https://doi.org/10.55059/ijm.2022.1.1/4.
- R.B. Albadarneh, A.K. Alomari, N. Tahat, I.M. Batiha, Analytic Solution of Nonlinear Singular Bvp With MultiOrder Fractional Derivatives in Electrohydrodynamic Flows, TWMS J. Appl. Eng. Math. 11 (2021), 1125-1137. https://hdl.handle.net/11729/3261.
- I.M. Batiha, Z. Chebana, T.-E. Oussaeif, A. Ouannas, I.H. Jebril, On a Weak Solution of a Fractional-order Temporal Equation, Math. Stat. 10 (2022), 1116–1120. https://doi.org/10.13189/ms.2022.100522.
- N. Anakira, Z. Chebana, T.E. Oussaeif, I.M. Batiha, A. Ouannas, A Study of a Weak Solution of a Diffusion Problem for a Temporal Fractional Differential Equation, Nonlinear Funct. Anal. Appl. 27 (2022), 679–689. https://doi.org/10.22771/NFAA.2022.27.03.14.
- T. Hamadneh, A. Zraiqat, H. Al-Zoubi, M. Elbes, Sufficient Conditions and Bounding Properties for Control Functions Using Bernstein Expansion, Appl. Math. Inf. Sci. 14 (2020), 1-9.
- O. Taki-Eddine, B. Abdelfatah, A Priori Estimates for Weak Solution for a Time-Fractional Nonlinear ReactionDiffusion Equations With an Integral Condition, Chaos Solitons Fractals. 103 (2017), 79–89. https://doi.org/10.1016/j.chaos.2017.05.035.
- T.E. Oussaeif, A. Bouziani, Solvability of Nonlinear Viscosity Equation With a Boundary Integral Condition, J. Nonlinear Evol. Equ. Appl. 3 (2015), 31-45.
- T.E. Oussaeif, A. Bouziani, Solvability of Nonlinear Goursat Type Problem for Hyperbolic Equation with Integral Condition, Khayyam J. Math. 4 (2018), 198–213. https://doi.org/10.22034/kjm.2018.65161.
- S. Dhelis, A. Bouziani and T.-E. Oussaeif, Study of Solution for a Parabolic Integro-Differential Equation With the Second Kind Integral Condition, Int. J. Anal. Appl. 16 (2018), 569-593. https://doi.org/10.28924/2291-8639-16-2018-569.
- T.E. Oussaeif, A. Bouziani, Existence and Uniqueness of Solutions to Parabolic Fractional Differential Equations With Integral Conditions, Electron. J. Differ. Equ. 2014 (2014), 179.