Journal of Inverse and Ill-Posed Problems · 2012 · 17 citations · 0 references
Natural SciencesComputational EngineeringDifferential EquationsFinite Element AnalysisFinite Element MethodsBoundary ConditionsBoundary-value ProblemsInitial Value ProblemsInverse ProblemsInverse Problems In MechanicsPartial Differential EquationsElliptic Boundary-value ProblemsElliptic FunctionsInverse Boundary-value ProblemsInverse Problem TheoryNeumann Boundary ConditionsNeumann ProblemsUniqueness In Elliptic EquationsUniqueness In Inverse Problems
Abstract. The two inverse problems of determining an unknown parameter in a nonhomogeneous part of the equation for an abstract second-order elliptic equation in a Banach space with boundary conditions of Bitsadze–Samarski type are considered. For the first problem we use the conditions of Dirichlet, and for the second problem we use the conditions of Neumann. Theorems of existence and uniqueness of solutions for both direct and inverse problems are proved. Explicit formulas for the solutions are obtained.