Global solution and blow-up solution for a nonlinear damped beam with source term

Article

Abstract

A nonlinear damped system with boundary input and output, which also has source term, is studied in this paper. It is proved that under some conditions the system has global solution and blow-up solution.

Keywords

Nonlinear hyperbolic system boundary input and output global solution blow-up solution 

MR Subject Classification

35L35 35G30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    V Georgiev, G Todorova. Existence of a solution of the wave equation with nonlinear damping and source terms, J Differential Equations, 1994, 109: 295–308.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    J H Hao, S J Li. Global solution and blowup solution for a nonlinear string with boundary input and output, Nonlinear Anal, 2007, 66: 131–137.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    N A Larkin. Global solvability of boundary value problem for a class of quasilinear hyperbolic equations, Siberian Math J, 1981, 22: 82–88.CrossRefGoogle Scholar
  4. [4]
    H Levine. Instability and nonexistence of global solutions to nonlinear wave equations of the form Pu tt = Au + F(u), Trans Amer Math Soc, 1974, 192: 1–21.MATHMathSciNetGoogle Scholar
  5. [5]
    H Levine. Some additional remarks on the nonexistence of global solutions to nonlinear wave equation, SIAM J Math Anal, 1974, 5: 138–146.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    H A Levine, J Serrin. A global nonexistence theorem for quasilinear evolution equations with dissipation, Arch Rational Mech Anal, 1997, 137: 341–361.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    H A Levine, P Pucci, J Serrin. Some remarks on global nonexistence for nonautonomous abstract evolution equations, Contemp Math, 1997, 208: 253–263.MathSciNetGoogle Scholar
  8. [8]
    H A Levine, G Todorova. Blow up of solutions of the Cauchy problem for a wave equation with nonlinear damping and source terms and positive initial energy, Proc Amer Math Soc, 2000, 129: 793–805.CrossRefMathSciNetGoogle Scholar
  9. [9]
    K Nishihara, H J Zhao. Decay properties of solutions to the Cauchy problem for the damped wave equation with absorption, J Math Anal Appl, 2006, 313: 598–610.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    P F Yao, G Weiss. Global smooth solutions and exponential stability for a nonlinear beam, SIAM J Control Optim, 2007, 45: 1931–1964.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanxi UniversityTaiyuanChina

Personalised recommendations