Well-posedness for the biharmonic scattering problem for a penetrable obstacle

2025/06/11 by Rafael Ceja Ayala, Ayala, Rafael Ceja, Isaac Harris +3 · 1 citation
Engineering · Mathematics · #35J35 #47A40 #74H25 #74J05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Thermoelastic and Magnetoelastic Phenomena #Ultrasonics and Acoustic Wave Propagation

paper · pdf · doi:10.48550/arxiv.2506.10176

openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address the direct scattering problem for a penetrable obstacle in an infinite elastic two--dimensional Kirchhoff--Love plate. Under the assumption that the plate's thickness is small relative to the wavelength of the incident wave, the propagation of perturbations on the plate is governed by the two-dimensional biharmonic wave equation, which we study in the frequency domain. With the help of an operator factorization, the scattering problem is analyzed from the perspective of a coupled boundary value problem involving the Helmholtz and modified Helmholtz equations. Well-posedness and reciprocity relations for the problem are established. Numerical examples for some special cases are provided to validate the theoretical findings.

Citations

• Direct sampling for recovering a clamped cavity from biharmonic far field data
• A novel boundary integral formulation for the biharmonic wave scattering problem
• On an inverse problem for the plate equation with passive measurement
• A highly accurate boundary integral method for the elastic obstacle scattering problem
• On an inverse boundary problem arising in brain imaging
• Determining the first order perturbation of a polyharmonic operator on admissible manifolds
• A fully discrete Calderon Calculus for the two-dimensional elastic wave equation
• A fully discrete Calderon Calculus for two dimensional time harmonic waves
• Determining a first order perturbation of the biharmonic operator by partial boundary measurements
• A Nyström flavored Calderón Calculus of order three for two dimensional waves, time-harmonic and transient

Cited by

• Factorization method for the biharmonic scattering problem for an absorbing penetrable scatterer

Related

• Analysis of the transmission eigenvalue problem for biharmonic scattering considering penetrable scatterers
• The obstacle scattering for the biharmonic equation
• A novel boundary integral formulation for the biharmonic wave scattering problem
• Factorization method for the biharmonic scattering problem for an absorbing penetrable scatterer
• Existence of transmission eigenvalues for biharmonic scattering by a clamped planar region