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<p>Combing the weak KAM method for contact Hamiltonian systems and the theory of viscosity solutions for Hamilton–Jacobi equations, we study the Lyapunov stability and instability of viscosity solutions for evolutionary contact Hamilton–Jacobi equation in the first part. In the second part, we study the existence and multiplicity of time-periodic solutions.</p>

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Stability of Solutions to Contact Hamilton–Jacobi Equation on the Circle

  • 期刊论文

  • 发表日期：

    2025年11月15日

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  • Yang Xu,
  • Jun Yan,
  • Kai Zhao

摘要

Combing the weak KAM method for contact Hamiltonian systems and the theory of viscosity solutions for Hamilton–Jacobi equations, we study the Lyapunov stability and instability of viscosity solutions for evolutionary contact Hamilton–Jacobi equation in the first part. In the second part, we study the existence and multiplicity of time-periodic solutions.