Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order
Davron Aslonqulovich Juraev, Ali Shokri, Daniela Marian
Abstract
We study, in this paper, the Cauchy problem for matrix factorizations of the Helmholtz equation in the space Rm. Based on the constructed Carleman matrix, we find an explicit form of the approximate solution of this problem and prove the stability of the solutions.
Topics & Concepts
MathematicsCauchy problemMatrix (chemical analysis)Order (exchange)Cauchy distributionCauchy matrixStability (learning theory)Initial value problemSpace (punctuation)Mathematical analysisApplied mathematicsType (biology)Helmholtz equationPure mathematicsElliptic partial differential equationCauchy boundary conditionPartial differential equationComputer scienceMaterials scienceMachine learningEconomicsComposite materialFree boundary problemBoundary value problemOperating systemBiologyFinanceEcologyNumerical methods in inverse problemsDifferential Equations and Boundary ProblemsAlgebraic and Geometric Analysis