Discrete regularization and convergence of the inverse problem for 1+1\n dimensional wave equation

2018/03/28 by Jussi Korpela, Korpela, Jussi, Matti Lassas +3
Computer Science · Mathematics · #35L05 #35R30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1803.10541

openalex publication_date 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An inverse boundary value problem for the 1+1 dimensional wave equation\n(\∂_t² - c(x)² \∂_x²)u(x,t)=0, x\∈\ℝ₊ is\nconsidered. We give a discrete regularization strategy to recover wave speed\nc(x) when we are given the boundary value of the wave, u(0,t), that is\nproduced by a single pulse-like source. The regularization strategy gives an\napproximative wave speed widetilde c, satisfying a H "older type estimate\n\‖ widetilde c-c\‖\≤ C \ε^\γ, where \ε is the noise\nlevel.\n

Related

• Convergence of an inverse problem for discrete wave equations
• An inverse problem for a semi-linear wave equation: a numerical study
• Regularization of an Ill-posed Cauchy Problem for the Wave Equation (Fourier Method)
• Recovering a (1+1)-dimensional wave equation from a single white noise boundary measurement
• Stability of an inverse problem for the discrete wave equation and convergence results