Energy Decay of Solutions for a System of Higher-Order Kirchhoff Type Equations
Yıl 2019,
Sayı: 29, 89 - 100, 30.12.2019
Erhan Pişkin
,
Ezgi Harman
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
Erhan Pişkin
,
Ezgi Harman
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.