KaydedilenlerDerginizi ekleyin

Dergiler / Middle East Journal of Science / 2018 / Cilt: 4 - Sayı: 2

BLOW UP OF SOLUTIONS FOR A TIMOSHENKO EQUATION WITH DAMPING TERMS

Erhan PİŞKİN
Hazal YÜKSEKKAYA
Sayfa
70–80
Yayın Tarihi
2018-12-27
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We show that the blow up of solutions with positive and negative initial energy.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this work, we studied the following equation u_{tt}+△²u-M(‖∇u‖²)△u-△u_{t}+u_{t}=|u|^{q-1}u regard to initial and Dirichlet boundary condition.
📊
Temel Bulgular & Veri:In this work, we studied the following equation u_{tt}+△²u-M(‖∇u‖²)△u-△u_{t}+u_{t}=|u|^{q-1}u regard to initial and Dirichlet boundary condition.
💡
Sonuç & Katkı:We show that the blow up of solutions with positive and negative initial energy.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Timoshenko equation · Blow up · Damping term

Abstract

In this work, we studied the following equation u_{tt}+△²u-M(‖∇u‖²)△u-△u_{t}+u_{t}=|u|^{q-1}u regard to initial and Dirichlet boundary condition. We show that the blow up of solutions with positive and negative initial energy.

🔖

Bu Makaleye Atıf Yap

PİŞKİN, E., YÜKSEKKAYA, H. (2018). BLOW UP OF SOLUTIONS FOR A TIMOSHENKO EQUATION WITH DAMPING TERMS. Middle East Journal of Science, Cilt: 4 - Sayı: 2, 70–80. https://ajindex.com/articles/691553

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. Adams, R.A., Fournier, J.J.F. (2003).
  2. Sobolev Spaces, Academic Press,
  3. New York. Chen, W., Zhou, Y. (2009). Global nonexistence for a semilinear Petrovsky equation, Nonlinear Anal., 70, 3203-3208. Doshi,C. (1979). On the Analysis of the Timoshenko Beam Theory with and without internal damping, Thesis, Rochester Institute of Technology. Esquivel-Avila, J.A. (2010). Dynamic analysis of a nonlinear Timoshenko equation, Abstract and Applied Analysis, 2011, 1-36.
  4. Esquivel-Avila, J.A. (2013). Global attractor for a nonlinear Timoshenko equation with source terms, Mathematical Sciences, 1-8.
  5. Georgiev, V., Todorova, G. (1994). Existence of a solution of the wave equation with nonlinear damping and source term, Journal of Differential Equations, 109, 295-308.
  6. Levine, H.A. (1974). Instability and nonexistence of global solutions to nonlinear wave equations of the form Pu_{tt}=-Au+F(u), Trans. Amer. Math. Soc., 192, 1-21.
  7. Levine, H.A. (1974). Some additional remarks on the nonexistence of global solutions to nonlinear wave equations, SIAM Journal on Applied Mathematics, 5, 138-146.
  8. Li, M.R., Tsai, L.Y. (2003). Existence and nonexistence of global solutions of some system of semilinear wave equations, Nonlinear Anal., 54 (8), 1397-1415.
  9. Messaoudi, S.A. (2001). Blow up in a nonlinearly damped wave equation, Mathematische Nachrichten, 231, 105-111.
  10. Messaoudi, S.A. (2002). Global existence and nonexistence in a system of Petrovsky, J. Math. Anal. Appl., 265(2), 296-308.
  11. Pişkin, E. (2015). Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms, Open Math., 13, 408-420.
  12. Pişkin E., Irkıl, N. (2016). Blow up of Positive Initial-Energy Solutions for the Extensible Beam Equation with Nonlinear Damping and Source terms, Ser. Math. Inform., 31(3), 645-654.
  13. Timoshenko, S.P. (1921). On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars, Philosophical Magazine and Journal of Science, 6(41), 744-746.
  14. Vitillaro, E. (1999). Global existence theorems for a class of evolution equations with dissipation, Arch. Rational Mech. Anal., 149, 155-182.
  15. Wu, S.T., Tsai, L.Y. (2009). On global solutions and blow-up of solutions for a nonlinearly damped Petrovsky system, Taiwanese J. Math., 13 (2A), 545-558.