Araştırma Makalesi
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Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations

Yıl 2019, Sayı: 29, 89 - 100, 30.12.2019

Öz

In this work, we considered a
system of higher-order Kirchhoff type equations with initial and boundary
conditions in a bounded domain. Under suitable conditions, we proved an energy
decay result by Nakao's inequality techniques.

Destekleyen Kurum

Dicle University

Proje Numarası

ZGEF.18.009

Kaynakça

  • G. Kirchhoff, Mechanik, Teubner, (1883).
  • S. T. Wu, On Decay and Blow-Up of Solutions for a System of Nonlinear Wave Equations, Journal of Mathematical Analysis and Applications 394 (2012) 360-377.
  • X. Han, M. Wang, Global Existence and Blow-Up of Solutions for a System of Nonlinear Viscoelastic Wave Equations with Damping and Source, Nonlinear Analysis 7 (2009) 5427-5450.
  • S. A. Messaoudi, B. Said-Houari, Global Nonexistence of Positive Initial-Energy Solutions of a System of Nonlinear Viscoelastic Wave Equations with Damping and Source Terms, Journal of Mathematical Analysis and Applications 365 (2010) 277-287.
  • B. Said-Houari, S. A. Messaoudi, A. Guesmia, General Decay of Solutions of a Nonlinear System of Viscoelastic Wave Equations, Nonlinear Differential Equations and Applications 18 (2011) 659-684.
  • E. Pişkin, A Lower Bound for the Blow-Up Time of a System of Viscoelastic Wave Equations with Nonlinear Damping and Source Terms, Journal of Nonlinear Functional Analysis 2017 (2017) 1-9.
  • E. Pişkin, Global Nonexistence of Solutions for a System of Viscoelastic Wave Equations with Weak Damping Terms, Malaya Journal of Matematik 3(2) (2015) 168-174.
  • Y. Ye, Global Existence and Energy Decay for a Coupled System of Kirchhoff Type Equations with Damping and Source Terms, Acta Mathematicae Applicatae Sinica, English Series 32(3) (2016) 731-738.
  • Q. Gao, F. Li, Y. Wang, Blow-Up of the Solution for Higher-Order Kirchhoff-Type Equations with Nonlinear Dissipation, Central European Journal of Mathematic 9(3) (2011) 686-698.
  • E. Hesameddini, Y. Khalili, Blow-Up of the Solution for Higher-Order Integro-Differential Equation with Nonlinear Dissipation, Applied Mathematical Sciences 5(72) (2011) 3575-3583.
  • E. Pişkin, N. Polat, Exponential Decay and Blow up of a Solution for a System of Nonlinear Higher-Order Wave Equations, American Institute of Physics Conference Proceedings 1470 (2012) 118-121.
  • E. Pişkin, N. Polat, Blow Up of Positive Initial-Energy Solutions for a Coupled Nonlinear Higher-Order Hyperbolic Equations, American Institute of Physics Conference Proceedings 1676 (2015) 1-8.
  • E. Pişkin, N. Polat, Global Existence and Exponential Decay of Solutions for a Class of System of Nonlinear Higher-Order Wave Equations with Strong Damping, Journal of Advanced Research in Applied Mathematics 4(4) (2012) 26-36.
  • E. Pişkin, N. Polat, On the Decay of Solutions for a Nonlinear Higher-Order Kirchhoff-Type Hyperbolic Equation, Journal of Advanced Research in Applied Mathematics 5(2) (2013) 107-116.
  • Y. Ye, Global Existence and Energy Decay Estimate of Solutions for a Higher-Order Kirchhoff Type Equation with Damping and Source Term, Nonlinear Analysis: Real World Applications 14 (2013) 2059-2067.
  • Y. Ye, Existence and Asymptotic Behavior of Global Solutions for Aclass of Nonlinear Higher-Order Wave Equation, Journal of Inequalities and Applications 2010 (2010) 1-14.
  • Y. Ye, Global Existence and Asymptotic Behavior of Solutions for a System of Higher-Order Kirchhoff-Type Equations, Electronic Journal of Qualitative Theory of Differential Equations 20 (2015) 1-12.
  • J. Zhou, X. Wang, X. Song, C. Mu, Global Existence and Blowup of Solutions for a Class of Nonlinear Higher-Order Wave Equations, Zeitschrift für angewandte Mathematik und Physik 63 (2012) 461-473.
  • R. A. Adams, J. J. F. Fournier, Sobolev Spaces, Academic Press, New York, 2003.
  • E. Pişkin, Sobolev Uzayları, Seçkin Yayıncılık (2017) (In Turkish).
  • M. Nakao, A Difference Inequality and Its Application to Nonlinear Evolution Equations, Journal of the Mathematical Society of Japan 30(4) (1978) 747-762.
Yıl 2019, Sayı: 29, 89 - 100, 30.12.2019

Öz

Proje Numarası

ZGEF.18.009

Kaynakça

  • G. Kirchhoff, Mechanik, Teubner, (1883).
  • S. T. Wu, On Decay and Blow-Up of Solutions for a System of Nonlinear Wave Equations, Journal of Mathematical Analysis and Applications 394 (2012) 360-377.
  • X. Han, M. Wang, Global Existence and Blow-Up of Solutions for a System of Nonlinear Viscoelastic Wave Equations with Damping and Source, Nonlinear Analysis 7 (2009) 5427-5450.
  • S. A. Messaoudi, B. Said-Houari, Global Nonexistence of Positive Initial-Energy Solutions of a System of Nonlinear Viscoelastic Wave Equations with Damping and Source Terms, Journal of Mathematical Analysis and Applications 365 (2010) 277-287.
  • B. Said-Houari, S. A. Messaoudi, A. Guesmia, General Decay of Solutions of a Nonlinear System of Viscoelastic Wave Equations, Nonlinear Differential Equations and Applications 18 (2011) 659-684.
  • E. Pişkin, A Lower Bound for the Blow-Up Time of a System of Viscoelastic Wave Equations with Nonlinear Damping and Source Terms, Journal of Nonlinear Functional Analysis 2017 (2017) 1-9.
  • E. Pişkin, Global Nonexistence of Solutions for a System of Viscoelastic Wave Equations with Weak Damping Terms, Malaya Journal of Matematik 3(2) (2015) 168-174.
  • Y. Ye, Global Existence and Energy Decay for a Coupled System of Kirchhoff Type Equations with Damping and Source Terms, Acta Mathematicae Applicatae Sinica, English Series 32(3) (2016) 731-738.
  • Q. Gao, F. Li, Y. Wang, Blow-Up of the Solution for Higher-Order Kirchhoff-Type Equations with Nonlinear Dissipation, Central European Journal of Mathematic 9(3) (2011) 686-698.
  • E. Hesameddini, Y. Khalili, Blow-Up of the Solution for Higher-Order Integro-Differential Equation with Nonlinear Dissipation, Applied Mathematical Sciences 5(72) (2011) 3575-3583.
  • E. Pişkin, N. Polat, Exponential Decay and Blow up of a Solution for a System of Nonlinear Higher-Order Wave Equations, American Institute of Physics Conference Proceedings 1470 (2012) 118-121.
  • E. Pişkin, N. Polat, Blow Up of Positive Initial-Energy Solutions for a Coupled Nonlinear Higher-Order Hyperbolic Equations, American Institute of Physics Conference Proceedings 1676 (2015) 1-8.
  • E. Pişkin, N. Polat, Global Existence and Exponential Decay of Solutions for a Class of System of Nonlinear Higher-Order Wave Equations with Strong Damping, Journal of Advanced Research in Applied Mathematics 4(4) (2012) 26-36.
  • E. Pişkin, N. Polat, On the Decay of Solutions for a Nonlinear Higher-Order Kirchhoff-Type Hyperbolic Equation, Journal of Advanced Research in Applied Mathematics 5(2) (2013) 107-116.
  • Y. Ye, Global Existence and Energy Decay Estimate of Solutions for a Higher-Order Kirchhoff Type Equation with Damping and Source Term, Nonlinear Analysis: Real World Applications 14 (2013) 2059-2067.
  • Y. Ye, Existence and Asymptotic Behavior of Global Solutions for Aclass of Nonlinear Higher-Order Wave Equation, Journal of Inequalities and Applications 2010 (2010) 1-14.
  • Y. Ye, Global Existence and Asymptotic Behavior of Solutions for a System of Higher-Order Kirchhoff-Type Equations, Electronic Journal of Qualitative Theory of Differential Equations 20 (2015) 1-12.
  • J. Zhou, X. Wang, X. Song, C. Mu, Global Existence and Blowup of Solutions for a Class of Nonlinear Higher-Order Wave Equations, Zeitschrift für angewandte Mathematik und Physik 63 (2012) 461-473.
  • R. A. Adams, J. J. F. Fournier, Sobolev Spaces, Academic Press, New York, 2003.
  • E. Pişkin, Sobolev Uzayları, Seçkin Yayıncılık (2017) (In Turkish).
  • M. Nakao, A Difference Inequality and Its Application to Nonlinear Evolution Equations, Journal of the Mathematical Society of Japan 30(4) (1978) 747-762.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Araştırma Makalesi
Yazarlar

Erhan Pişkin 0000-0001-6587-4479

Ezgi Harman Bu kişi benim 0000-0002-1863-2909

Proje Numarası ZGEF.18.009
Yayımlanma Tarihi 30 Aralık 2019
Gönderilme Tarihi 14 Ekim 2019
Yayımlandığı Sayı Yıl 2019 Sayı: 29

Kaynak Göster

APA Pişkin, E., & Harman, E. (2019). Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations. Journal of New Theory(29), 89-100.
AMA Pişkin E, Harman E. Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations. JNT. Aralık 2019;(29):89-100.
Chicago Pişkin, Erhan, ve Ezgi Harman. “Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations”. Journal of New Theory, sy. 29 (Aralık 2019): 89-100.
EndNote Pişkin E, Harman E (01 Aralık 2019) Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations. Journal of New Theory 29 89–100.
IEEE E. Pişkin ve E. Harman, “Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations”, JNT, sy. 29, ss. 89–100, Aralık 2019.
ISNAD Pişkin, Erhan - Harman, Ezgi. “Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations”. Journal of New Theory 29 (Aralık 2019), 89-100.
JAMA Pişkin E, Harman E. Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations. JNT. 2019;:89–100.
MLA Pişkin, Erhan ve Ezgi Harman. “Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations”. Journal of New Theory, sy. 29, 2019, ss. 89-100.
Vancouver Pişkin E, Harman E. Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations. JNT. 2019(29):89-100.


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