SavedAdd your journal

Journals / Turkish Journal of Mathematics / 2018 / Cilt: 42 - Sayı: 3

Continuous dependence of solutions to the strongly damped nonlinear Klein–Gordon equation

Şevket GÜR
Mesude Elif UYSAL
Pages
904–910
Publication Date
2022-11-05
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)

It is proved that the solution depends continuously on changes in the damping terms, diffusion,mass, and nonlinearity effect term in the $H^1$ norm.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This article is devoted to the study of the initial-boundary value problem for the strongly damped nonlinearKlein–Gordon equation.
📊
Key Findings & Data:This article is devoted to the study of the initial-boundary value problem for the strongly damped nonlinearKlein–Gordon equation.
💡
Conclusion & Impact:It is proved that the solution depends continuously on changes in the damping terms, diffusion,mass, and nonlinearity effect term in the $H^1$ norm.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

This article is devoted to the study of the initial-boundary value problem for the strongly damped nonlinearKlein–Gordon equation. It is proved that the solution depends continuously on changes in the damping terms, diffusion,mass, and nonlinearity effect term in the $H^1$ norm.

🔖

Cite This Article

GÜR, Ş., UYSAL, M. E. (2022). Continuous dependence of solutions to the strongly damped nonlinear Klein–Gordon equation. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 3, 904–910. https://ajindex.com/articles/607797

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (18)

  1. Ames KA, Straughan B. Non-Standard and Improperly Posed Problems. Mathematics in Science and Engineering Series. New York, NY, USA: Academic Press, 1997
  2. Avrin JD. Convergence properties of the strongly damped nonlinear KleinGordon equation. J Differ Equations 1987; 67: 243-255
  3. Ball JM. Finite time blow-up in nonlinear problems. In: Crandall MG, editor. Nonlinear Evolution Equations. New York, NY, USA: Academic Press, 1978, pp. 189-205
  4. Bellomo N, Preziosi L. Modelling Mathematical Methods and Scientific Computation. Boca Raton, FL, USA: CRC Press, 1995
  5. Cazenave T. Uniform estimates for solutions of nonlinear Klein-Gordon equations. J Funct Anal 1985; 1: 36-55
  6. Cazenave T, Haraux A. An Introduction to Semilinear Evolution Equations. Oxford Lecture Series in Mathematics and Its Applications. Oxford, UK: Oxford University Press, 1998
  7. Çelebi AO, G¨ur S¸, Kalantarov VK. Structural stability and decay estimate for marine riser equations. Math Comput Model 2011; 11-12: 3182-3188
  8. Gao P, Guo BL. The time-periodic solution for a 2D dissipative Klein–Gordon equation. J Math Anal Appl 2004; 296: 286-294
  9. Ginibre J, Velo G. The global Cauchy problem for the nonlinear Klein-Gordon equation. Ann I H Poincare-An 1989; 6: 15-35
  10. Güleç İ, Gür Ş. Continuous dependence of solutions to fourth-order nonlinear wave equation. Hacet J Math Stat 2016; 45: 367-371
  11. Ha TG, Park JY. Global existence and uniform decay of a damped Klein-Gordon equation in a noncylindrical domain. Nonlinear Anal 2011; 74: 577-584
  12. Klainerman S. Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions. Commun Pur Appl Math 1985; 38: 631-641
  13. Lions JL. Quelques methodes de resolution des problemes aux limites non lineaires. Paris, France: Dunod, 1969 (in French)
  14. Nakao M. Energy decay to the Cauchy problem of nonlinear Klein-Gordon equations with a sublinear dissipative term. Adv Math Sci Appl 2009; 19: 479-501
  15. Pecher H. L p -Absch¨atzungen und klassiche L¨osungen f¨ur nichtlineare Wellengleichungen. I. Math Z 1976; 150: 159-183 (in German)
  16. Polat N, Taskesen H. On the existence of global solutions for a nonlinear Klein-Gordon equation, Filomat 2014; 28: 1073-1079
  17. Strauss WA. Nonlinear scattering theory at low energy. J Funct Anal 1981; 41: 110-133
  18. Strauss WA. Nonlinear Wave Equations. In: CBMS Regional Conference Series in Mathematics. Published for the Conference