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March 5, 2026Filomat0 citationsOpen Access

On the well-posedness of mild solutions to certain nonlinear wave equations

NHNguyễn Minh HảiNLNguyen Hoang LucNBNghia T. Bui

Key Points

  • This research focuses on the existence and uniqueness of solutions to the Cauchy problem for the Love equation under varying conditions.
  • Analyzed the Cauchy problem for the Love equation
  • Established conditions for existence and uniqueness
  • Investigated continuous dependence on parameters
  • Demonstrated convergence of the Love equation solution to the wave equation solution.
  • Existence of solutions confirmed under various nonlinear conditions
  • Uniqueness of solutions established
  • Continuous dependence of solutions on parameters shown
  • Demonstrated convergence to the wave equation solution.

Abstract

We aredevoted to the study of the Cauchy problem for Love equation. We establish the existence and uniqueness of the solution under different conditions imposed on the nonlinear source function. We analyze the continuous dependence of the solution with respect to the parameters involved in the equation. Additionally, in this paper, we also shown that the solution to the Love equation converges to the solution of the wave equation.

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Cite This Study

Hải et al. (2025) studied this question.

synapsesocial.com/papers/69a91d6dd6127c7a504c02aehttps://doi.org/10.2298/fil2519723m
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