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Year 2020, Volume: 8 Issue: 1, 216 - 222, 15.04.2020

Erhan Pişkin Fatma Ekinci

Abstract

References

  • [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

Year 2020, Volume: 8 Issue: 1, 216 - 222, 15.04.2020

Erhan Pişkin Fatma Ekinci

Abstract

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.



Keywords

Blow up Exponential growth

References

  • [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.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Erhan Pişkin

Fatma Ekinci

Publication Date April 15, 2020
Submission Date July 15, 2019
Acceptance Date April 25, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

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. April 2020;8(1):216-222.
Chicago Pişkin, Erhan, and Fatma Ekinci. “Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation With Multiple Nonlinearities”. Konuralp Journal of Mathematics 8, no. 1 (April 2020): 216-22.
EndNote Pişkin E, Ekinci F (April 1, 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 and F. Ekinci, “Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities”, Konuralp J. Math., vol. 8, no. 1, pp. 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 (April 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 and Fatma Ekinci. “Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation With Multiple Nonlinearities”. Konuralp Journal of Mathematics, vol. 8, no. 1, 2020, pp. 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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