FINITE-TIME BLOW UP OF SOLUTIONS FOR A FOURTH-ORDER VISCOELASTIC WAVE EQUATION WITH DAMPING TERMS

Le Thi Mai Thanh; Le Thi Phuong Ngoc; Nguyen Huu Nhan; Nguyen Thanh Long

doi:10.11948/20230162

2023 Volume 13 Issue 6

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Le Thi Mai Thanh, Le Thi Phuong Ngoc, Nguyen Huu Nhan, Nguyen Thanh Long. FINITE-TIME BLOW UP OF SOLUTIONS FOR A FOURTH-ORDER VISCOELASTIC WAVE EQUATION WITH DAMPING TERMS[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3558-3591. doi: 10.11948/20230162

Citation:

Le Thi Mai Thanh, Le Thi Phuong Ngoc, Nguyen Huu Nhan, Nguyen Thanh Long. FINITE-TIME BLOW UP OF SOLUTIONS FOR A FOURTH-ORDER VISCOELASTIC WAVE EQUATION WITH DAMPING TERMS[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3558-3591. doi: 10.11948/20230162

FINITE-TIME BLOW UP OF SOLUTIONS FOR A FOURTH-ORDER VISCOELASTIC WAVE EQUATION WITH DAMPING TERMS

1.
Faculty of Mathematics and Computer Science, Ho Chi Minh City University of Science, 227 Nguyen Van Cu Street, 700000, Vietnam
2.
Vietnam National University, 700000, Vietnam
3.
Department of Basic Science, Nguyen Tat Thanh University, 300A Nguyen Tat Thanh Street, 700000, Vietnam
4.
University of Khanh Hoa, 01 Nguyen Chanh Street, 650000, Vietnam
5.
Ho Chi Minh City University of Foreign Languages and Information Technology, 828 Su Van Hanh Street, 700000, Vietnam

Author Bio: Email: ltmthanh@ntt.edu.vn(L. T. M. Thanh); Email: ngoc1966@gmail.com(L. T. P. Ngoc); Email: longnt2@gmail.com(N. T. Long)
Corresponding author: Email: nhannh1@huflit.edu.vn(N. H. Nhan)

Abstract

Abstract

In this paper, a class of fourth-order viscoelastic wave equations with damping terms is studied. First, the local existence and uniqueness of weak solutions for the proposed problem are proved by the linear approximation and the Faedo-Galerkin method. Next, a special case of the original problem is considered. Then, under some suitablely sufficient conditions on the relaxation functions and by using contrary arguments, we show that the corresponding problem in this case does not admit any global solutions. Ultimately, we prove the finite-time blow up of solutions in case of negative initial energy.
- Fourth-order wave equation /
- Faedo-Galerkin method /
- finite-time blow up /
- linear approximation /
- damping term
MSC: 35A01, 35A02, 35G31, 35L35

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References

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