Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지

A NUMERICAL METHOD FOR THE PROBLEM OF COEFFICIENT IDENTIFICATION OF THE WAVE EQUATION BASED ON A LOCAL OBSERVATION ON THE BOUNDARY

  • Shirota, Kenji (Department of Mathematics Sciences, Ibaraki University)
  • Published : 2001.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this paper is to propose a numerical algorithm for the problem of coefficient identification of the scalar wave equation based on a local observation on the boundary: Determine the unknown coefficient function with the knowledge of simultaneous Dirichlet and Neumann boundary values on a part of boundary. To find the unknown coefficient function, the unknown Neumann boundary value is also identified. We recast our inverse problem to variational problem. The gradient method is applied to find the minimizing functions. We confirm the effectiveness of our algorithm by numerical experiments.

Keywords

References

  1. Pacific J. Mathematics v.16 Minimization of functions having Lipschitz continuous first partial derivatives L. Armijo
  2. J. Math. Anal. Appl. v.150 On Continuous Dependence for an Inverse Initial Boundary Value Problem for the Wave Equation Z. Sun
  3. J. Math. Pures Appl. v.78 Uniqueness and stability in multidimensional hyperbolic inverse problems M. Yamamoto