Scholarlink

<p>We develop uniquely solvable second kind boundary integral equations systems for solving the transmission problem associated with linear elastic waves propagation in two-dimensional isotropic and homogeneous media. With the help of the Günter derivative, the transmission boundary conditions are rewritten in such a way the physical system can be reduced to a compact perturbation of an invertible zero-order operator—a lower off-diagonal perturbation of identity—without regularization procedure. Inspired by the Müller formulation developed for the electromagnetic case, hypersingular and strong singularities of the boundary integral operator kernels are cancelled out by considering particular combinations of the Calderón projections on the contact boundary curve. Irregular frequencies do not occur with this method. Existence and uniqueness can be established on either a single function space or on a mixed regularity solution space.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the Müller boundary integral equation method for solving contact problems in 2D linear elasticity

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月24日

查看全文
  • Frédérique Le Louër

摘要

We develop uniquely solvable second kind boundary integral equations systems for solving the transmission problem associated with linear elastic waves propagation in two-dimensional isotropic and homogeneous media. With the help of the Günter derivative, the transmission boundary conditions are rewritten in such a way the physical system can be reduced to a compact perturbation of an invertible zero-order operator—a lower off-diagonal perturbation of identity—without regularization procedure. Inspired by the Müller formulation developed for the electromagnetic case, hypersingular and strong singularities of the boundary integral operator kernels are cancelled out by considering particular combinations of the Calderón projections on the contact boundary curve. Irregular frequencies do not occur with this method. Existence and uniqueness can be established on either a single function space or on a mixed regularity solution space.