SavedAdd your journal

Journals / Konuralp Journal of Mathematics / 2026 / Volume: 8 Issue: 1

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

Erhan Pişkin
Fatma Ekinci
Pages
—
Publication Date
2020-04-15
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We prove a nonexistence of global solutions and exponential growth of solution with negative initial energy.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we investigate a class of doubly nonlinear parabolic systems with Krichhoff-type.
📊
Key Findings & Data:In this paper, we investigate a class of doubly nonlinear parabolic systems with Krichhoff-type.
💡
Conclusion & Impact:We prove a nonexistence of global solutions and exponential growth of solution with negative initial energy.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Blow up · Exponential growth

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.

🔖

Cite This Article

Pişkin, E., Ekinci, F. (2020). Blow Up and Growth of Solutions for A Parabolic Type Kirchhoff Equation with Multiple Nonlinearities. Konuralp Journal of Mathematics, Volume: 8 Issue: 1. https://ajindex.com/articles/1521690

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  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.