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<p>We consider the wave equation for the Laplace operator with potential, initial data, and inhomogeneous Dirichlet boundary condition. We establish the existence of a weak solution by using traces and extension domains. We prove the existence, uniqueness, and consistency of a very weak solution for the wave equation with singularities in the potential, initial data, source term, boundary, and boundary condition.</p>

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Singular Klein–Gordon Equation on a Bounded Domain

  • 期刊论文

  • 发表日期：

    2025年6月7日

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  • Michael Ruzhansky,
  • Alibek Yeskermessuly

摘要

We consider the wave equation for the Laplace operator with potential, initial data, and inhomogeneous Dirichlet boundary condition. We establish the existence of a weak solution by using traces and extension domains. We prove the existence, uniqueness, and consistency of a very weak solution for the wave equation with singularities in the potential, initial data, source term, boundary, and boundary condition.