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Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term

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Abstract

We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the kernel function and the nonlinear terms. Finally, under suitable conditions to obtain the global solution, we prove the general decay property with positive initial energy for this global solution.

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Acknowledgement

The authors wish to express their sincere thanks to the editor and the referees for the valuable comments and suggestions leading to the improvement of the paper.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam

    Doan Thi Nhu Quynh & Nguyen Thanh Long

  2. Vietnam National University, Linh Trung Ward, Thu Duc City, Ho Chi Minh City, Vietnam

    Doan Thi Nhu Quynh & Nguyen Thanh Long

  3. Faculty of Applied Sciences, Ho Chi Minh City University of Food Industry, 140 Le Trong Tan Str., Tay Thanh Ward, Tan Phu Dist., Ho Chi Minh City, Vietnam

    Doan Thi Nhu Quynh

  4. Nguyen Tat Thanh University, 300A Nguyen Tat Thanh Str., Dist. 4, Ho Chi Minh City, Vietnam

    Nguyen Huu Nhan

  5. University of Khanh Hoa, 01 Nguyen Chanh Str., Nha Trang City, Vietnam

    Le Thi Phuong Ngoc

Authors
  1. Doan Thi Nhu Quynh
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  2. Nguyen Huu Nhan
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  3. Le Thi Phuong Ngoc
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  4. Nguyen Thanh Long
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Corresponding author

Correspondence to Nguyen Thanh Long.

Additional information

This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number B2020-18-01.

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Quynh, D.T.N., Nhan, N.H., Ngoc, L.T.P. et al. Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term. Appl Math 68, 209–254 (2022). https://doi.org/10.21136/AM.2022.0200-21

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  • DOI: https://doi.org/10.21136/AM.2022.0200-21

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