Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 8 Sayı: 1, 216 - 222, 15.04.2020

Öz

Kaynakça

  • [1] Y. Han, Q. Li, Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy, Computers and Mathematics with Applications, 75, (2018), 3283-3297.
  • [2] Y. Han, W. Gao, Z. Sun, H. Li, Upper and lower bounds of blow-up time to a parabolic type Kirchhoff equation with arbitrary initial energy, Computers and Mathematics with Applications, 76, (2018), 2477-2483.
  • [3] N. H. Tuan, D. H. Q. Nam, T. M. N. Vo, On a backward problem for the Kirchhoff’s model of parabolic type, Computers and Mathematics with Applications, 77, (2019), 115-33.
  • [4] L. Dawidowski, The quasilinear parabolic Kirchhoff equation, Open Mathematics, 15, (2017), 382–392.
  • [5] M. Gobbino, Quasilinear degenerate parabolic equations of Kirchhoff type, Mathematical Methods in the Applied Science, 22(5), (1999), 375–388.
  • [6] S. Kundu, K. A. Pani, M. Khebchareon, On Kirchhoff’s model of parabolic type, Numerical Functional Analysis and Optimization, 37(6), (2016), 719–752.
  • [7] N. H. Chang, M. Chipot, Nonlinear nonlocal evolution problems, RACSAM, Rev. R. Acad. Cien. Ser. A. Mat., 97, (2003), 393–415.
  • [8] S. Zheng, M. Chipot, Asymptotic behavior of solutions to nonlinear parabolic equations with nonlocal terms, Asymptotic Analysis, 45, (2005), 301–312.
  • [9] Y. Ye, Global existence and energy decay for a coupled system of Kirchhoff type equations with damping and source terms, Acta Mathematicae Applicatae Sinica, 32(3), (2016), 731-738.
  • [10] K. Narasimha, Nonlinear vibration of an elastic string, Journal of Sound and Vibration, 8, (1968), 134–146.
  • [11] E. Pişkin, F. Ekinci, Nonexistence of global solutions for coupled Kirchhoff-type equations with degenerate dampings terms, Journal of Nonlinear Functional Analysis, 2018, (2018), 1-14.
  • [12] K. Ono, Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings, Journal of Differential Equations, 137, (1997), 273-301.
  • [13] B. Cheng, X. Wu, Existence results of positive solutions of Kirchhoff type problems, Nonlinear Analysis, 71, (2009), 4883-4892.
  • [14] Y. Zhijian, Longtime behavior of the Kirchhoff type equation with strong damping on Rn, Journal of Differential Equations, 242, (2007), 269-286.
  • [15] M. O. Korpusov, A. G. Sveshnikov, Sufficent close-to-necessary conditions for the blowup of solutions to a strongly nonlinear generalized Boussinesq equation, Computational Mathematics and Mathematical Physics, 48(9), (2008), 1591-1599.
  • [16] O. Ladyzenskaia, V. Solonikov, N. Uraltceva, Linear and quasilinear parabolic equations of second order, Translation of Mathematical Monographs. AMS, Rhode Island, 1968.

Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities

Yıl 2020, Cilt: 8 Sayı: 1, 216 - 222, 15.04.2020

Öz

In this paper, we investigate a class of doubly nonlinear parabolic systems with Krichhoff-type. We prove a nonexistence of global solutions and exponential growth of solution with negative initial energy.



Kaynakça

  • [1] Y. Han, Q. Li, Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy, Computers and Mathematics with Applications, 75, (2018), 3283-3297.
  • [2] Y. Han, W. Gao, Z. Sun, H. Li, Upper and lower bounds of blow-up time to a parabolic type Kirchhoff equation with arbitrary initial energy, Computers and Mathematics with Applications, 76, (2018), 2477-2483.
  • [3] N. H. Tuan, D. H. Q. Nam, T. M. N. Vo, On a backward problem for the Kirchhoff’s model of parabolic type, Computers and Mathematics with Applications, 77, (2019), 115-33.
  • [4] L. Dawidowski, The quasilinear parabolic Kirchhoff equation, Open Mathematics, 15, (2017), 382–392.
  • [5] M. Gobbino, Quasilinear degenerate parabolic equations of Kirchhoff type, Mathematical Methods in the Applied Science, 22(5), (1999), 375–388.
  • [6] S. Kundu, K. A. Pani, M. Khebchareon, On Kirchhoff’s model of parabolic type, Numerical Functional Analysis and Optimization, 37(6), (2016), 719–752.
  • [7] N. H. Chang, M. Chipot, Nonlinear nonlocal evolution problems, RACSAM, Rev. R. Acad. Cien. Ser. A. Mat., 97, (2003), 393–415.
  • [8] S. Zheng, M. Chipot, Asymptotic behavior of solutions to nonlinear parabolic equations with nonlocal terms, Asymptotic Analysis, 45, (2005), 301–312.
  • [9] Y. Ye, Global existence and energy decay for a coupled system of Kirchhoff type equations with damping and source terms, Acta Mathematicae Applicatae Sinica, 32(3), (2016), 731-738.
  • [10] K. Narasimha, Nonlinear vibration of an elastic string, Journal of Sound and Vibration, 8, (1968), 134–146.
  • [11] E. Pişkin, F. Ekinci, Nonexistence of global solutions for coupled Kirchhoff-type equations with degenerate dampings terms, Journal of Nonlinear Functional Analysis, 2018, (2018), 1-14.
  • [12] K. Ono, Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings, Journal of Differential Equations, 137, (1997), 273-301.
  • [13] B. Cheng, X. Wu, Existence results of positive solutions of Kirchhoff type problems, Nonlinear Analysis, 71, (2009), 4883-4892.
  • [14] Y. Zhijian, Longtime behavior of the Kirchhoff type equation with strong damping on Rn, Journal of Differential Equations, 242, (2007), 269-286.
  • [15] M. O. Korpusov, A. G. Sveshnikov, Sufficent close-to-necessary conditions for the blowup of solutions to a strongly nonlinear generalized Boussinesq equation, Computational Mathematics and Mathematical Physics, 48(9), (2008), 1591-1599.
  • [16] O. Ladyzenskaia, V. Solonikov, N. Uraltceva, Linear and quasilinear parabolic equations of second order, Translation of Mathematical Monographs. AMS, Rhode Island, 1968.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Erhan Pişkin

Fatma Ekinci

Yayımlanma Tarihi 15 Nisan 2020
Gönderilme Tarihi 15 Temmuz 2019
Kabul Tarihi 25 Nisan 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 1

Kaynak Göster

APA Pişkin, E., & Ekinci, F. (2020). Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities. Konuralp Journal of Mathematics, 8(1), 216-222.
AMA Pişkin E, Ekinci F. Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities. Konuralp J. Math. Nisan 2020;8(1):216-222.
Chicago Pişkin, Erhan, ve Fatma Ekinci. “Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation With Multiple Nonlinearities”. Konuralp Journal of Mathematics 8, sy. 1 (Nisan 2020): 216-22.
EndNote Pişkin E, Ekinci F (01 Nisan 2020) Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities. Konuralp Journal of Mathematics 8 1 216–222.
IEEE E. Pişkin ve F. Ekinci, “Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities”, Konuralp J. Math., c. 8, sy. 1, ss. 216–222, 2020.
ISNAD Pişkin, Erhan - Ekinci, Fatma. “Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation With Multiple Nonlinearities”. Konuralp Journal of Mathematics 8/1 (Nisan 2020), 216-222.
JAMA Pişkin E, Ekinci F. Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities. Konuralp J. Math. 2020;8:216–222.
MLA Pişkin, Erhan ve Fatma Ekinci. “Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation With Multiple Nonlinearities”. Konuralp Journal of Mathematics, c. 8, sy. 1, 2020, ss. 216-22.
Vancouver Pişkin E, Ekinci F. Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities. Konuralp J. Math. 2020;8(1):216-22.
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