On the Approximate Solution of the Cauchy Problem in a Multidimensional Unbounded Domain
Davron Aslonqulovich Juraev, Ali Shokri, Daniela Marian
Abstract
In this paper, the Carleman matrix is constructed, and based on it we found explicitly a regularized solution of the Cauchy problem for the matrix factorization of the Helmholtz equation in a multidimensional unbounded domain in Rm,(m=2k,k≥2). The corresponding theorems on the stability of the solution of problems are proved.
Topics & Concepts
MathematicsDomain (mathematical analysis)Matrix (chemical analysis)Cauchy problemStability (learning theory)Helmholtz equationFactorizationCauchy distributionMathematical analysisCauchy matrixApplied mathematicsPure mathematicsInitial value problemCauchy boundary conditionBoundary value problemComputer scienceAlgorithmNeumann boundary conditionMaterials scienceMachine learningComposite materialNumerical methods in inverse problemsDifferential Equations and Boundary ProblemsHeat Transfer and Mathematical Modeling