충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제35권2호
  • /
  • Pages.137-147
  • /
  • 2022
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

BLOW-UP PHENOMENA OF ARBITRARY POSITIVE INITIAL ENERGY SOLUTIONS FOR A VISCOELASTIC WAVE EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS

  • Yi, Su-Cheol (Department of Mathematics Changwon National University)
  • 투고 : 2022.02.25
  • 심사 : 2022.05.01
  • 발행 : 2022.05.15
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we considered the Dirichlet initial boundary value problem of a nonlinear viscoelastic wave equation with nonlinear damping and source terms, and investigated finite time blow-up phenomena of the solutions to the equation with arbitrary positive initial data, under suitable conditions.

키워드

과제정보

The author would like to deeply thank all the reviewers for their insightful and constructive comments.

참고문헌

  1. D. D. Ang and A. P. N. Dinh, Strong solutions of quasilinear wave equation with non-linear damping, SIAM J. Math. Anal., 19 (1988), 337-347. https://doi.org/10.1137/0519024
  2. V. Georgiev and G. Todorova, Existence of solutions of the wave equation with non-linear damping and source terms, J. Differntial Equations, 109 (1994), 295-308. https://doi.org/10.1006/jdeq.1994.1051
  3. S. Kavashima and Y. Shibata, Global existence and exponential stability of small solutions to non-linear viscoelasticity, Commun. Math. Phys., 148 (1992), 189-208. https://doi.org/10.1007/BF02102372
  4. H. A. Levine, Instability and nonexistene of global solutions of nonlinear wave equation of the form Putt = Au + F(u), Trans. Amer. Math. Soc., 192 (1974), 1-21. https://doi.org/10.1090/S0002-9947-1974-0344697-2
  5. H. A. Levine, Some additional remarks on the nonexistence of global solutions to nonlinear wave equation, SIAM J. Math. Anal., 5 (1974), 138-146. https://doi.org/10.1137/0505015
  6. S. A. Messaoudi, Blow up in a nonlinearly damped wave equation, Math. Nachr., 231 (2001), no. 1, 1-7. https://doi.org/10.1002/1522-2616(200111)231:1<105::AID-MANA105>3.0.CO;2-I
  7. S. A. Messaoudi and B. S. Houari, Global non-existence of solutions of a class of wave equations with non-linear damping and source terms, Math. Method. Appl. Sci., 27 (2004), no. 14, 1687-1696. https://doi.org/10.1002/mma.522
  8. H. Song, Blow up of arbitrarily positive initial energy solutions for a viscoelastic wave equation, Nonlinear Anal-RWA, 26 (2015), 306-314. https://doi.org/10.1016/j.nonrwa.2015.05.015
  9. E. Vitillaro, Global non-existence theorems for a class of evolution equations with dissipation, Arch. Ration. Mech. Anal., 149 (1999), 155-182. https://doi.org/10.1007/s002050050171
  10. Z. Yang, Blow up of solutions for a class of non-linear evolution equations with non-linear damping and source terms, Math. Meth. Appl. Sci., 25 (2002), 825-833. https://doi.org/10.1002/mma.312
  11. R. Zeng, C. Mu and S. Zhou, A blow-up result for Kirchhoff-type equations with high energy, Math. Method. Appl. Sci., 34 (2011), no. 4, 479-486. https://doi.org/10.1002/mma.1374