Simultaneous inversion of two initial values for a time‐fractional diffusion‐wave equation
Yun Zhang, Ting Wei, Yuan‐Xiang Zhang
Abstract
Abstract This study is devoted to recovering two initial values for a time‐fractional diffusion‐wave equation from boundary Cauchy data. We provide the uniqueness result for recovering two initial values simultaneously by the method of Laplace transformation and analytic continuation. And then we use a nonstationary iterative Tikhonov regularization method to solve the inverse problem and propose a finite dimensional approximation algorithm to find good approximations to the initial values. Numerical examples in one‐ and two‐dimensional cases are provided to show the effectiveness of the proposed method.
Topics & Concepts
Tikhonov regularizationMathematicsContinuationUniquenessMathematical analysisLaplace transformRegularization (linguistics)Inversion (geology)Inverse problemCauchy distributionDiffusion equationWave equationInitial value problemApplied mathematicsBoundary value problemComputer scienceProgramming languageStructural basinService (business)EconomyPaleontologyBiologyEconomicsArtificial intelligenceFractional Differential Equations SolutionsNumerical methods in inverse problemsNumerical methods in engineering