Asymptotic Analysis - Volume 138, issue 1-2

Authors: Badawi, Haidar | Alsayed, Hawraa

Article Type: Research Article

Abstract: In this paper, we consider a one dimensional thermoelastic Timoshenko system in which the heat flux is given by Cattaneo’s law and acts locally on the bending moment with a time delay. We prove its well-posedness, strong stability, and polynomial stability.

Keywords: Timoshenko system, Cattaneo’s law, strong stability, polynomial stability, frequency domain approach, time delay

DOI: 10.3233/ASY-231888

Citation: Asymptotic Analysis, vol. 138, no. 1-2, pp. 1-26, 2024

Authors: Sá Barreto, Antônio | Stefanov, Plamen

Article Type: Research Article

Abstract: We study the inverse problem of recovery a nonlinearity f ( t , x , u ) , which is compactly supported in x , in the semilinear wave equation u tt − Δ u + f ( t , x , u ) = 0 . We probe the medium with either complex or real-valued harmonic waves of wavelength ∼ h and amplitude ∼ 1 . They propagate in a regime where the nonlinearity affects the subprincipal but not the principal term, except for the zeroth harmonics. …We measure the transmitted wave when it exits supp x f . We show that one can recover f ( t , x , u ) when it is an odd function of u , and we can recover α ( x ) when f ( t , x , u ) = α ( x ) u 2 m . This is done in an explicit way as h → 0 . Show more

DOI: 10.3233/ASY-231890

Citation: Asymptotic Analysis, vol. 138, no. 1-2, pp. 27-68, 2024

Authors: Bouhoufani, Oulia | Messaoudi, Salim A. | Alahyane, Mohamed

Article Type: Research Article

Abstract: In this paper, we consider a coupled system of two biharmonic equations with damping and source terms of variable-exponent nonlinearities, supplemented with initial and mixed boundary conditions. We establish an existence and uniqueness result of a weak solution, under suitable assumptions on the variable exponents. Then, we show that solutions with negative-initial energy blow up in finite time. To illustrate our theoritical findings, we present two numerical examples.

Keywords: Biharmonic operator, Existence, Blow up, Coupled system, Variable exponent, Weak solution

DOI: 10.3233/ASY-231891

Citation: Asymptotic Analysis, vol. 138, no. 1-2, pp. 69-99, 2024

Authors: Al-Mahdi, Adel M.

Article Type: Research Article

Abstract: In this study, we consider a one-dimensional Timoshenko system with two damping terms in the context of the second frequency spectrum. One damping is viscoelastic with infinite memory, while the other is a non-linear frictional damping of variable exponent type. These damping terms are simultaneously and complementary acting on the shear force in the domain. We establish, for the first time to the best of our knowledge, explicit and general energy decay rates for this system with infinite memory. We use Sobolev embedding and the multiplier approach to get our decay results. These results generalize and improve some earlier related …results in the literature. Show more

Keywords: Timoshenko system, second frequency spectrum, multiplier method, infinite memory, exponential and polynomial decay, variable exponents

DOI: 10.3233/ASY-231892

Citation: Asymptotic Analysis, vol. 138, no. 1-2, pp. 101-133, 2024

Authors: Nguyen-Tien, Hoang

Article Type: Research Article

Abstract: We study the optimal convergence rate for the homogenization problem of convex Hamilton–Jacobi equations when the Hamitonian is periodic with respect to spatial and time variables, and notably time-dependent. We prove a result similar to that of (Tran and Yu (2021 )), which means the optimal convergence rate is also O ( ε ) .

Keywords: Hamilton–Jacobi equations, homogenization, spatio-temporal periodic setting, optimal convergent rate, viscosity solutions

DOI: 10.3233/ASY-241898

Citation: Asymptotic Analysis, vol. 138, no. 1-2, pp. 135-150, 2024