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<p>In this paper, we examine a general model of Love-type damped wave equations that includes the <i>p</i>-Laplacian and a memory term. Firstly, by utilizing linearization techniques, the Faedo-Galerkin method, and arguments of compactness, we establish the existence and uniqueness of solutions for the problem. Next, the techniques and estimations presented in [Appl. Math. 68 (2) (2023) 209-254] are used to obtain the continuous dependence of solutions on relaxation functions and nonlinear components of the problem. Furthermore, under several appropriate assumptions, a finite-time blow-up of solutions with negative initial energy is also proved. Finally, we discuss some open problems that arise from our findings.</p>

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Blow-up and continuous dependence of solutions for a class of Love-type damped wave equations with p-Laplacian and memory term

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Nguyen Huu Nhan,
  • Nguyen Son Hong Hanh,
  • Nguyen Anh Triet,
  • Le Thi Phuong Ngoc,
  • Nguyen Thanh Long

摘要

In this paper, we examine a general model of Love-type damped wave equations that includes the p-Laplacian and a memory term. Firstly, by utilizing linearization techniques, the Faedo-Galerkin method, and arguments of compactness, we establish the existence and uniqueness of solutions for the problem. Next, the techniques and estimations presented in [Appl. Math. 68 (2) (2023) 209-254] are used to obtain the continuous dependence of solutions on relaxation functions and nonlinear components of the problem. Furthermore, under several appropriate assumptions, a finite-time blow-up of solutions with negative initial energy is also proved. Finally, we discuss some open problems that arise from our findings.