Communications in Partial Differential Equations · 2001 · 55 citations · 10 references
Natural SciencesMathematicsComputational Fluid DynamicsDifferential EquationsFinite Element AnalysisBoundary ConditionsBoundary-value ProblemsInitial Value ProblemsPartial Differential EquationsVariational FormulationWeak FormulationElliptic Boundary-value ProblemsElliptic Partial Differential EquationsLinearizationNonlinear Boundary-value ProblemsNonlinear Partial Differential EquationsParabolic Partial Differential EquationsSingular Boundary-value ProblemsUniqueness Of Solutions
We prove uniqueness of the term c(u,p) of partial differential equations −Δu + c(u, ∇u) = 0 and ∂ t u − Δu + c(u, ∇u) = 0 with the Dirichlet-to-Neumann map given on a part of the lateral boundary. We use a linearization method and singular solutions in the boundary reconstruction of the linearized equations
10