Blow up for Initial-Boundary Value Problem of Wave Equation with a Nonlinear Memory in 1-D

【Author】

Ning-An LAI;Jianli LIU;Jinglei ZHAO;Department of Mathematics, Lishui University;Department of Mathematics, Shanghai University;College of Education, Lishui University;

【Institution】

Department of Mathematics, Lishui University;Department of Mathematics, Shanghai University;College of Education, Lishui University;

【Abstract】

The present paper is devoted to studying the initial-boundary value problem of a 1-D wave equation with a nonlinear memory: u_(tt) - u_(xx) = 1/ Γ(1 - γ) ∫_0~t (t - s)~(-γ)|u(s)|~pds. The blow up result will be established when p > 1 and 0 < γ < 1, no matter how small the initial data are, by introducing two test functions and a new functional.

【Keywords】

Blow up;;Wave equation;;Nonlinear memory;;Initial-boundary value problem

References

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Springer Journals Database

Total: 25 articles

  • [1] Yi ZHOU School of Mathematical Sciences, Fudan University, Shanghai 200433, China., Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions, Chinese Annals of Mathematics, 2007 (02)
  • [2] Borislav T. Yordanov;;Qi S. Zhang, Finite time blow up for critical wave equations in high dimensions, Journal of Functional Analysis, 2005 (2)
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  • [4] Fritz John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Mathematica, 1979 (1)

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