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Yıl 2021, , 492 - 510, 11.04.2021

Abdelmajid Issaq , Qiaozhen Ma Ahmed Eshag Mohamed

https://doi.org/10.15672/hujms.614217

Öz

Kaynakça

  • [1] A.D. Abdelmajid, E.M. Ahmed and Q. Ma, Random attractors for Stochastic strongly damped non-autonomous wave equations with memory and multiplicative noise, Open J. Math. Anal. 3, 50–70, 2019.
  • [2] L. Arnold and H. Crauel, Random dynamical systems lyapunov exponents proceedings oberwolfach, in: Lecture Notes in Mathematics, 1486, 1–22, 1990.
  • [3] P.W. Bates, K. Lu and B. Wang, Random attractors for stochastic reaction diffusion equations on unbounded domains, J. Differ. Equ. 246, 845–869, 2009.
  • [4] T. Caraballo and J. Langa, On the upper semi-continuity of cocycle attractors for non-autonomous and random dynamical systems, Discr. Contin. Dyn. Impuls. Syst. Ser. Math. Anal. 10 491–513, 2003.
  • [5] T. Caraballo, J. Langa and J. Robinson, Upper semi-continuity of attractors for small random perturbations of dynamical systems, Commun. Part. Differ. Equ. 23, 1557– 1581, 1998.
  • [6] F. Chen, B. Guo and P. Wang, Long time behavior of strongly damped nonlinear wave equations, J. Differ. Equ. 147, 231–241,1998.
  • [7] J.W. Cholewa and T. Dlotko, Strongly damped wave equation in uniform spaces, Nonlinear Anal. 64 174–187, 2006.
  • [8] I. Chueshov, Monotone Random Systems Theory and Applications, Springer-Verlag, New York, 2002.
  • [9] H. Crauel, A. Debussche, and F. Flandoli, Random attractors, J. Dyn. Differ. Equ. 9, 307–341, 1997.
  • [10] H. Crauel and F. Fladli Crauel, Attractors for a random dynamical systems, Probab. Theory Related Fields 100, 365–393, 1994.
  • [11] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.
  • [12] J. Duan, K. Lu and B. Schmalfuss, Invariant manifolds for stochastic partial differ- ential equations, Ann. Probab. 31, 2109–2135, 2003.
  • [13] M.M. Fadlallah, A.D. Abdelmajid, E.M. Ahmed, M.Y.A. Bakhet and Q. Ma, Random attractors for semilinear reaction diffusion equation with distribution derivatives and multiplicative noise, Open J. Math. Sci. 4, 126–141, 2020.
  • [14] X. Fan, Random attractors for damped stochastic wave equations with multiplicative noise, Int. J. Math. 19, 421-437, 2008.
  • [15] F. Flandoli and B. Schmalfuss, Random attractors for the 3-D stochastic Navier- Stokes equation with multiplicative noise, Stoch. Rep. 59, 21–45, 1996.
  • [16] J.M. Ghidaglia and A. Marzocchi, Longtime behaviour of strongly damped wave equa- tions, global attractors and their dimension, SIAM J. Math. Anal. 22, 879–895, 1991.
  • [17] J.K. Hale and G. Raugel, Upper semi-continuity of the attractor for a singularly perturbed hyperbolic equation, J. Differ. Equ. 73 (2), 197–214, 1988.
  • [18] V. Kalantarov and S. Zelik, Finite-dimensional attractors for the quasi-linear strongly- damped wave equation, J. Differ. Equ. 247, 1120–1155, 2009.
  • [19] H. Li, Y. You and J. Tu, Random attractors and averaging for nonautonomous sto- chastic wave equations with nonlinear damping, J. Differ. Equ. 258, 148–190, 2015.
  • [20] H. Li and S. Zhou, One-dimensional global attractor for strongly damped wave equa- tions, Commun. Nonlinear Sci. Numer. Simul. 12, 784–793, 2007.
  • [21] H. Li and S. Zhou, On non-autonomous strongly damped wave equations with a uni- form attractor and Some averaging, J. Math. Anal. Appl. 341, 791–802, 2008.
  • [22] P. Massatt, Limiting behavior for strongly damped nonlinear wave equations, J. Differ. Equ. 48, 334–349, 1983.
  • [23] H. Morimoto, Attractors of probability measures for semi-linear stochastic evolution equations, Stoch. Anal. Appl. 10, 205–212, 1992.
  • [24] V. Pata and S. Zelik, Smooth attractors for strongly damped wave equations, Nonlin- earity, 19, 1495–1506, 2006.
  • [25] A. Pazy, Semigroup of linear operators and applications to partial differential equa- tions, Appl. Math. Sci., Springer, New York, 1983.
  • [26] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1997.
  • [27] B. Wang, Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems, J. Part. Differ. Equ. 253, 1544–1583, 2012.
  • [28] B.Wang, Random attractors for non-autonomous stochastic wave equations with mul- tiplicative noise, Discrete Contin. Dyn. Syst. 34, 269–300, 2014.
  • [29] B. Wang, Existence and upper semi-continuity of attractors for stochastic equations with deterministic non-autonomous terms, Stoch. Dyn. 14 (4), 1450009, 2014.
  • [30] B. Wang and X. Gao, Random attractors for wave equations on unbounded domains, Discrete Contin. Dyn. Syst. Spec. 2009, 800–809, 2009.
  • [31] Z. Wang and S. Zhou, Asymptotic behavior of stochastic strongly wave equation on unbounded domains, J. Appl. Math. Phys. 3, 338-357, 2015.
  • [32] M. Yang and C. Sun, Dynamics of strongly damped wave equations in locally uniform spaces: attractors and asymptotic regularity, Trans. Amer. Math. Soc. 361, 1069– 1101, 2009.
  • [33] M. Yang and C. Sun, Exponential attractors for the strongly damped wave equations, Nonlinear. Anal: Real World Appl. 11, 913–919, 2010.
  • [34] F. Yin and L. Liu, D-pullback attractor for a non-autonomous wave equation with additive noise on unbounded domains, J. Comput. Math. Appl. 68, 424–438, 2014.
  • [35] S. Zhou and X. Fan, Kernel sections for non-autonomous strongly damped wave equa- tions, J. Math. Anal. Appl. 275, 850–869, 2002.

Existence of random attractors for strongly damped wave equations with multiplicative noise unbounded domain

Yıl 2021, , 492 - 510, 11.04.2021

Abdelmajid Issaq , Qiaozhen Ma Ahmed Eshag Mohamed

https://doi.org/10.15672/hujms.614217

Öz

In this paper, we establish the existence of a random attractor for a random dynamical system generated by the non-autonomous wave equation with strong damping and multiplicative noise when the nonlinear term satisfies a critical growth condition.

Anahtar Kelimeler

stochastic strong damped wave equation asymptotic behavior of solutions random attractor random dynamical system

Kaynakça

  • [1] A.D. Abdelmajid, E.M. Ahmed and Q. Ma, Random attractors for Stochastic strongly damped non-autonomous wave equations with memory and multiplicative noise, Open J. Math. Anal. 3, 50–70, 2019.
  • [2] L. Arnold and H. Crauel, Random dynamical systems lyapunov exponents proceedings oberwolfach, in: Lecture Notes in Mathematics, 1486, 1–22, 1990.
  • [3] P.W. Bates, K. Lu and B. Wang, Random attractors for stochastic reaction diffusion equations on unbounded domains, J. Differ. Equ. 246, 845–869, 2009.
  • [4] T. Caraballo and J. Langa, On the upper semi-continuity of cocycle attractors for non-autonomous and random dynamical systems, Discr. Contin. Dyn. Impuls. Syst. Ser. Math. Anal. 10 491–513, 2003.
  • [5] T. Caraballo, J. Langa and J. Robinson, Upper semi-continuity of attractors for small random perturbations of dynamical systems, Commun. Part. Differ. Equ. 23, 1557– 1581, 1998.
  • [6] F. Chen, B. Guo and P. Wang, Long time behavior of strongly damped nonlinear wave equations, J. Differ. Equ. 147, 231–241,1998.
  • [7] J.W. Cholewa and T. Dlotko, Strongly damped wave equation in uniform spaces, Nonlinear Anal. 64 174–187, 2006.
  • [8] I. Chueshov, Monotone Random Systems Theory and Applications, Springer-Verlag, New York, 2002.
  • [9] H. Crauel, A. Debussche, and F. Flandoli, Random attractors, J. Dyn. Differ. Equ. 9, 307–341, 1997.
  • [10] H. Crauel and F. Fladli Crauel, Attractors for a random dynamical systems, Probab. Theory Related Fields 100, 365–393, 1994.
  • [11] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.
  • [12] J. Duan, K. Lu and B. Schmalfuss, Invariant manifolds for stochastic partial differ- ential equations, Ann. Probab. 31, 2109–2135, 2003.
  • [13] M.M. Fadlallah, A.D. Abdelmajid, E.M. Ahmed, M.Y.A. Bakhet and Q. Ma, Random attractors for semilinear reaction diffusion equation with distribution derivatives and multiplicative noise, Open J. Math. Sci. 4, 126–141, 2020.
  • [14] X. Fan, Random attractors for damped stochastic wave equations with multiplicative noise, Int. J. Math. 19, 421-437, 2008.
  • [15] F. Flandoli and B. Schmalfuss, Random attractors for the 3-D stochastic Navier- Stokes equation with multiplicative noise, Stoch. Rep. 59, 21–45, 1996.
  • [16] J.M. Ghidaglia and A. Marzocchi, Longtime behaviour of strongly damped wave equa- tions, global attractors and their dimension, SIAM J. Math. Anal. 22, 879–895, 1991.
  • [17] J.K. Hale and G. Raugel, Upper semi-continuity of the attractor for a singularly perturbed hyperbolic equation, J. Differ. Equ. 73 (2), 197–214, 1988.
  • [18] V. Kalantarov and S. Zelik, Finite-dimensional attractors for the quasi-linear strongly- damped wave equation, J. Differ. Equ. 247, 1120–1155, 2009.
  • [19] H. Li, Y. You and J. Tu, Random attractors and averaging for nonautonomous sto- chastic wave equations with nonlinear damping, J. Differ. Equ. 258, 148–190, 2015.
  • [20] H. Li and S. Zhou, One-dimensional global attractor for strongly damped wave equa- tions, Commun. Nonlinear Sci. Numer. Simul. 12, 784–793, 2007.
  • [21] H. Li and S. Zhou, On non-autonomous strongly damped wave equations with a uni- form attractor and Some averaging, J. Math. Anal. Appl. 341, 791–802, 2008.
  • [22] P. Massatt, Limiting behavior for strongly damped nonlinear wave equations, J. Differ. Equ. 48, 334–349, 1983.
  • [23] H. Morimoto, Attractors of probability measures for semi-linear stochastic evolution equations, Stoch. Anal. Appl. 10, 205–212, 1992.
  • [24] V. Pata and S. Zelik, Smooth attractors for strongly damped wave equations, Nonlin- earity, 19, 1495–1506, 2006.
  • [25] A. Pazy, Semigroup of linear operators and applications to partial differential equa- tions, Appl. Math. Sci., Springer, New York, 1983.
  • [26] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1997.
  • [27] B. Wang, Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems, J. Part. Differ. Equ. 253, 1544–1583, 2012.
  • [28] B.Wang, Random attractors for non-autonomous stochastic wave equations with mul- tiplicative noise, Discrete Contin. Dyn. Syst. 34, 269–300, 2014.
  • [29] B. Wang, Existence and upper semi-continuity of attractors for stochastic equations with deterministic non-autonomous terms, Stoch. Dyn. 14 (4), 1450009, 2014.
  • [30] B. Wang and X. Gao, Random attractors for wave equations on unbounded domains, Discrete Contin. Dyn. Syst. Spec. 2009, 800–809, 2009.
  • [31] Z. Wang and S. Zhou, Asymptotic behavior of stochastic strongly wave equation on unbounded domains, J. Appl. Math. Phys. 3, 338-357, 2015.
  • [32] M. Yang and C. Sun, Dynamics of strongly damped wave equations in locally uniform spaces: attractors and asymptotic regularity, Trans. Amer. Math. Soc. 361, 1069– 1101, 2009.
  • [33] M. Yang and C. Sun, Exponential attractors for the strongly damped wave equations, Nonlinear. Anal: Real World Appl. 11, 913–919, 2010.
  • [34] F. Yin and L. Liu, D-pullback attractor for a non-autonomous wave equation with additive noise on unbounded domains, J. Comput. Math. Appl. 68, 424–438, 2014.
  • [35] S. Zhou and X. Fan, Kernel sections for non-autonomous strongly damped wave equa- tions, J. Math. Anal. Appl. 275, 850–869, 2002.
Toplam 35 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Abdelmajid Issaq 0000-0001-6938-0556

Qiaozhen Ma 0000-0003-2971-2442

Ahmed Eshag Mohamed 0000-0001-7429-4492

Yayımlanma Tarihi 11 Nisan 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Issaq, A., Ma, Q., & Mohamed, A. E. (2021). Existence of random attractors for strongly damped wave equations with multiplicative noise unbounded domain. Hacettepe Journal of Mathematics and Statistics, 50(2), 492-510. https://doi.org/10.15672/hujms.614217
AMA Issaq A, Ma Q, Mohamed AE. Existence of random attractors for strongly damped wave equations with multiplicative noise unbounded domain. Hacettepe Journal of Mathematics and Statistics. Nisan 2021;50(2):492-510. doi:10.15672/hujms.614217
Chicago Issaq, Abdelmajid, Qiaozhen Ma, ve Ahmed Eshag Mohamed. “Existence of Random Attractors for Strongly Damped Wave Equations With Multiplicative Noise Unbounded Domain”. Hacettepe Journal of Mathematics and Statistics 50, sy. 2 (Nisan 2021): 492-510. https://doi.org/10.15672/hujms.614217.
EndNote Issaq A, Ma Q, Mohamed AE (01 Nisan 2021) Existence of random attractors for strongly damped wave equations with multiplicative noise unbounded domain. Hacettepe Journal of Mathematics and Statistics 50 2 492–510.
IEEE A. Issaq, Q. Ma, ve A. E. Mohamed, “Existence of random attractors for strongly damped wave equations with multiplicative noise unbounded domain”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, ss. 492–510, 2021, doi: 10.15672/hujms.614217.
ISNAD Issaq, Abdelmajid vd. “Existence of Random Attractors for Strongly Damped Wave Equations With Multiplicative Noise Unbounded Domain”. Hacettepe Journal of Mathematics and Statistics 50/2 (Nisan 2021), 492-510. https://doi.org/10.15672/hujms.614217.
JAMA Issaq A, Ma Q, Mohamed AE. Existence of random attractors for strongly damped wave equations with multiplicative noise unbounded domain. Hacettepe Journal of Mathematics and Statistics. 2021;50:492–510.
MLA Issaq, Abdelmajid vd. “Existence of Random Attractors for Strongly Damped Wave Equations With Multiplicative Noise Unbounded Domain”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, 2021, ss. 492-10, doi:10.15672/hujms.614217.
Vancouver Issaq A, Ma Q, Mohamed AE. Existence of random attractors for strongly damped wave equations with multiplicative noise unbounded domain. Hacettepe Journal of Mathematics and Statistics. 2021;50(2):492-510.

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