The inverse problem for the heat equation with reflection of the argument and with a complex coefficient
Elmira Mussirepova, Abdissalam Sarsenbi, Abdizhahan Sarsenbi, Abdizhahan Sarsenbi, Abdizhahan Sarsenbi
Abstract
Abstract The paper is devoted to finding a solution and restoring the right-hand side of the heat equation with reflection of the argument in the second derivative, with a complex-valued variable coefficient. We prove a theorem on the Riesz basis property for eigenfunctions of the second-order differential operator with involution in the second derivative. We establish the existence and uniqueness of the solution of the studied problems by the method of separation of variables
Topics & Concepts
MathematicsUniquenessHeat equationMathematical analysisEigenfunctionDifferential operatorArgument (complex analysis)Inverse problemOperator (biology)Reflection (computer programming)Pure mathematicsEigenvalues and eigenvectorsPhysicsProgramming languageTranscription factorBiochemistryChemistryComputer scienceQuantum mechanicsGeneRepressorNumerical methods in inverse problemsadvanced mathematical theoriesDifferential Equations and Boundary Problems