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LONG TIME BEHAVIOR OF THE STRONGLY DAMPED WAVE EQUATION WITH p-LAPLACIAN IN ℝn

Yıl 2020, Cilt: 10 Sayı: 2, 471 - 482, 01.03.2020

Öz

In this paper, the initial value problem for the one dimensional strongly damped wave equation with p-Laplacian and localized damping in the whole space is concerned. Under the condition 2 < p < 4, the existence of weak local attractors for this problem in W1,p R ∩ H1 R  × L 2 R is proved

Kaynakça

  • Kalantarov, V., (1986), Attractors for some nonlinear problems of mathematical physics, Zap. Nauchn.
  • Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI), 152, pp. 50–54. Ghidaglia, J.M. and Marzocchi, A., (1991), Longtime behaviour of strongly damped wave equations, global attractors and their dimension, SIAM J. Math. Anal., 22, pp. 879–895.
  • Zhou, S., (1999), Global attractor for strongly damped nonlinear wave equations, Funct. Diff. Eqns., , pp. 451–470.
  • Carvalho, A.N. and Cholewa, J.W., (2002), Attractors for strongly damped wave equations with critical nonlinearities, Pacific J. Math., 207, pp. 287–310.
  • Pata, V. and Squassina, M., (2005), On the strongly damped wave equation, Commun. Math. Phys., , pp. 511–533.
  • Pata, V. and Zelik, S., (2006), Smooth attractors for strongly damped wave equations, Nonlinearity, , pp. 1495–1506.
  • Yang, M. and Sun, C., (2009), Attractors for strongly damped wave equations, Nonlinear Anal.: Real World Applications, 10, pp. 1097-1100.
  • Dell’Oro, F. and Pata, V., (2011), Long-term analysis of strongly damped nonlinear wave equations, Nonlinearity, 24, pp. 3413–3435.
  • Dell’Oro, F. and Pata, V., (2012), Strongly damped wave equations with critical nonlinearities, Non- linear Anal., 75, pp. 5723–5735.
  • Khanmamedov, A.Kh., (2011), Global attractors for strongly damped wave equations with displace- ment dependent damping and nonlinear source term of critical exponent, Discrete Contin. Dyn. Syst. Ser. A, 31, pp. 119–138.
  • Khanmamedov, A.Kh., (2014), Strongly damped wave equation with exponential nonlinearities, J. Math. Anal. Appl., 419, pp. 663–687.
  • Khanmamedov, A.Kh., (2008), On the existence of a global attractor for the wave equation with nonlinear strong damping perturbed by nonmonotone term, Nonlinear Anal., 69, pp. 3372-3385.
  • Chueshov, I. and Lasiecka, I., (2008), Long time behavior of second order evolution equations with nonlinear damping. Mem. Amer. Math. Soc., 195.
  • Chen, F., Guo, B. and Wang, P., (1998), Long time behavior of strongly damped nonlinear wave equations, J. Diff. Equations, 147, pp. 231-241.
  • Kalantarov, V. and Zelik, S., (2009), Finite-dimensional attractors for the quasi-linear strongly- damped wave equation, J. Diff. Equations, 247, pp. 1120-1155.
  • Khanmamedov, A.Kh., S¸en, Z., (2017), Attractors for the Strongly Damped Wave Equation with p-Laplacian, Mathematical Methods in the Applied Sciences, 40, pp. 4436-4447.
  • Feireisl, E., (1994), Attractors for semilinear damped wave equations on R3, Nonlinear Anal., 23, pp. –195.
  • Feireisl, E., (1995), Asymptotic behavior and attractors for a semilinear damped wave equation with supercritical exponent, Proc. Roy. Soc. Edinburgh, 125, pp. 1051–1062.
  • Belleri, V. and Pata, V., (2001), Attractors for semilinear strongly damped wave equations on R3
  • Discrete Contin. Dyn. Syst, 7, pp. 719–735. Conti, M., Pata, V. and Squassina, M., (2005), Strongly damped wave equations on Rwith critical nonlinearities, Commun. Appl. Anal., 9, pp. 61–176.
Yıl 2020, Cilt: 10 Sayı: 2, 471 - 482, 01.03.2020

Öz

Kaynakça

  • Kalantarov, V., (1986), Attractors for some nonlinear problems of mathematical physics, Zap. Nauchn.
  • Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI), 152, pp. 50–54. Ghidaglia, J.M. and Marzocchi, A., (1991), Longtime behaviour of strongly damped wave equations, global attractors and their dimension, SIAM J. Math. Anal., 22, pp. 879–895.
  • Zhou, S., (1999), Global attractor for strongly damped nonlinear wave equations, Funct. Diff. Eqns., , pp. 451–470.
  • Carvalho, A.N. and Cholewa, J.W., (2002), Attractors for strongly damped wave equations with critical nonlinearities, Pacific J. Math., 207, pp. 287–310.
  • Pata, V. and Squassina, M., (2005), On the strongly damped wave equation, Commun. Math. Phys., , pp. 511–533.
  • Pata, V. and Zelik, S., (2006), Smooth attractors for strongly damped wave equations, Nonlinearity, , pp. 1495–1506.
  • Yang, M. and Sun, C., (2009), Attractors for strongly damped wave equations, Nonlinear Anal.: Real World Applications, 10, pp. 1097-1100.
  • Dell’Oro, F. and Pata, V., (2011), Long-term analysis of strongly damped nonlinear wave equations, Nonlinearity, 24, pp. 3413–3435.
  • Dell’Oro, F. and Pata, V., (2012), Strongly damped wave equations with critical nonlinearities, Non- linear Anal., 75, pp. 5723–5735.
  • Khanmamedov, A.Kh., (2011), Global attractors for strongly damped wave equations with displace- ment dependent damping and nonlinear source term of critical exponent, Discrete Contin. Dyn. Syst. Ser. A, 31, pp. 119–138.
  • Khanmamedov, A.Kh., (2014), Strongly damped wave equation with exponential nonlinearities, J. Math. Anal. Appl., 419, pp. 663–687.
  • Khanmamedov, A.Kh., (2008), On the existence of a global attractor for the wave equation with nonlinear strong damping perturbed by nonmonotone term, Nonlinear Anal., 69, pp. 3372-3385.
  • Chueshov, I. and Lasiecka, I., (2008), Long time behavior of second order evolution equations with nonlinear damping. Mem. Amer. Math. Soc., 195.
  • Chen, F., Guo, B. and Wang, P., (1998), Long time behavior of strongly damped nonlinear wave equations, J. Diff. Equations, 147, pp. 231-241.
  • Kalantarov, V. and Zelik, S., (2009), Finite-dimensional attractors for the quasi-linear strongly- damped wave equation, J. Diff. Equations, 247, pp. 1120-1155.
  • Khanmamedov, A.Kh., S¸en, Z., (2017), Attractors for the Strongly Damped Wave Equation with p-Laplacian, Mathematical Methods in the Applied Sciences, 40, pp. 4436-4447.
  • Feireisl, E., (1994), Attractors for semilinear damped wave equations on R3, Nonlinear Anal., 23, pp. –195.
  • Feireisl, E., (1995), Asymptotic behavior and attractors for a semilinear damped wave equation with supercritical exponent, Proc. Roy. Soc. Edinburgh, 125, pp. 1051–1062.
  • Belleri, V. and Pata, V., (2001), Attractors for semilinear strongly damped wave equations on R3
  • Discrete Contin. Dyn. Syst, 7, pp. 719–735. Conti, M., Pata, V. and Squassina, M., (2005), Strongly damped wave equations on Rwith critical nonlinearities, Commun. Appl. Anal., 9, pp. 61–176.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Z. Şen Bu kişi benim

Yayımlanma Tarihi 1 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 2

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