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<p>We investigate the Smoluchowski–Kramers approximation for the one-dimensional periodic variational wave equation with state-dependent damping and additive noise. We show that weak “dissipative” solutions converge to solutions of a stochastic quasilinear parabolic equation.</p>

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A Smoluchowski–Kramers Approximation for the Stochastic Variational Wave Equation

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Billel Guelmame,
  • Julien Vovelle

摘要

We investigate the Smoluchowski–Kramers approximation for the one-dimensional periodic variational wave equation with state-dependent damping and additive noise. We show that weak “dissipative” solutions converge to solutions of a stochastic quasilinear parabolic equation.