On a Non-local Sobolev–Galpern-Type Equation Associated with Random Noise
Long Le Dinh, Duc Phuong Nguyen, Maria Alessandra Ragusa
Abstract
Abstract This paper aims to retrieve the initial value for a non-local fractional Sobolev–Galpern problem. The given data are subject to noise by the discrete random model. We show that the solution to the problem is ill-posed in the sense of Hadamard. In this paper, we applied the Fourier truncation method to construct the regularized solution. We estimate the convergence between the solution and the regularized solution. In addition, the numerical example is also proposed to assess the efficiency of the theory.
Topics & Concepts
MathematicsSobolev spaceHadamard transformTruncation (statistics)Type (biology)Applied mathematicsRandom noiseMathematical analysisNoise (video)Convergence (economics)Initial value problemAlgorithmStatisticsArtificial intelligenceImage (mathematics)BiologyEcologyEconomic growthComputer scienceEconomicsNumerical methods in inverse problemsNumerical methods in engineeringAdvanced Mathematical Modeling in Engineering