Autor

DOI:

https://doi.org/10.12775/TMNA.2021.039

Słowa kluczowe

Abstrakt

Bibliografia

M. Afilal, A. Guesmia, A. Soufyane and M. Zahri, On the exponential and polynomial stability for a linear Bresse system, Math. Methods Appl. Sci. 43, (2020), no. 5, 2626–2645.

S. Antontsev, Wave equation with p(x, t)-Laplacian and damping term: blow-up of solutions, C.R. Mec. 339 (2011), no. 12, 751–755.

S. Antontsev and J. Ferreira, Existence, uniqueness and blowup for hyperbolic equations with nonstandard growth conditions, Nonlinear Anal. Theory Methods Appl. 93 (2013), 62–77.

S. Antontsev and S. Shmarev, Evolution PDEs with nonstandard growth conditions: existence, uniqueness, localization, blowup, Atlantis Studies in Differential Equations, vol. 4, Atlantis Press, Paris, 2015.

A. Benaissa and S.A. Messaoudi, Exponential decay of solutions of a nonlinearly damped wave equation, Nonlinear Differ. Equ. Appl. 12 (2006), no. 4, 391–399.

Y. Chen, S. Levine and M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (2006), no. 4, 1383–1406.

S. Ghegal, I. Hamchi and S.A. Messaoudi , Global existence and stability of a nonlinear wave equation with variable-exponent nonlinearities, Appl. Anal. 99 (2020), no. 8, 1333–1343.

B. Guo and W. Gao, Blow-up of solutions to quasilinear hyperbolic equations with p(x, t)Laplacian and positive initial energy, C.R. Mec. 342 (2014), no. 9, 513–519.

J.H. Hassan, S.A. Messaoudi and M. Zahri, Existence and new general decay results for a viscoelastic-type Timoshenko system, Z. Anal. Anwend. 39 (2020), no. 2, 185–222.

V. Komornik, Exact Controllability and Stabilization. The Multiplier Method, Masson–John Wiley, Paris, 1994.

D. Lars, P. Harjulehto, P. Hasto and M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics, vol. 2017, Springer–Verlag, Berlin, Heidelberg, 2011.

I. Lasiecka, Stabilization of wave and plate-like equation with nonlinear dissipation on the boundary, J. Differential Equations 79 (1989), 340–381.

I. Lasiecka and D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping, Differential Integral Equations 6 (1993), no. 3, 507–533.

P. Martinez, A new method to obtain decay rate estimates for dissipative systems with localized damping, Rev. Mat. Complut. 12 (1999), no. 1, 251–283.

S.A. Messaoudi, J.H. Al-Smail and A.A. Talahmeh, Decay for solutions of a nonlinear damped wave equation with variable-exponent nonlinearities, Comput. Math. Appl. 76 (2018), 1863–1875.

S.A. Messaoudi and A.A. Talahmeh, A blow-up result for a nonlinear wave equation with variable-exponent nonlinearities, Appl. Anal. 96 (2017), no. 9, 1509–1515.

S.A. Messaoudi and A.A. Talahmeh, A blow-up result for a quasilinear wave equation with variable- exponent nonlinearities, Math. Meth. Appl. Sci. 40 (2017), 6976–6986.

S.A. Messaoudi and A.A. Talahmeh, On wave equation: Review and recent results, Arab. J. Math.7 (2018), 113–145.

S.A. Messaoudi, A.A. Talahmeh and J.H. Al-Smail, Nonlinear damped wave equation: existence and blow-up, Comput. Math. Appl., DOI: 10.1016/j.camwa.2017.07.048.

M.I. Mustafa and S.A. Messaoudi, General energy decay rates for a weakly damped wave equation, Commun. Math. Anal. 9 (2010), no. 2, 67–76.

M. Nakao, A difference inequality and its applications to nonlinear evolution equations, J. Math. Soc. Japan 30 (1978), 747–762.

M. Nakao, Remarks on the existence and uniqueness of global decaying solutions of the nonlinear dissipative wave equations, Math Z. 206 (1991), 265–275.

M. Nakao, Decay of solutions of the wave equation with a local nonlinear dissipation, Math. Ann. 305 (1996), no. 3, 403–417.

E. Zuazua, Exponential decay for the semi-linear wave equation with locally distributed damping, Comm. Partial Differential Equations 15 (1990), 205–235.

Opublikowane

2022-06-12

Jak cytować

1.
& . Topological Methods in Nonlinear Analysis [online]. 12 czerwiec 2022, T. 59, nr 2B, s. 851–866. [udostępniono 22.7.2024]. DOI 10.12775/TMNA.2021.039.

Numer

Dział

Articles

Statystyki

Liczba wyświetleń i pobrań: 0
Liczba cytowań: 0