Boundary controllability for a degenerate and singular wave equation
Brahim Allal, Alhabib Moumni, Jawad Salhi
Abstract
In this paper, we deal with the boundary controllability of a one‐dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. Exact boundary controllability is proved in the range of both subcritical and critical potentials and for sufficiently large time, through a boundary controller acting away from the degenerate/singular point. By duality argument, we reduce the problem to an observability estimate for the corresponding adjoint system, which is proved by means of the multiplier method and new Hardy‐type inequalities.
Topics & Concepts
ControllabilityMathematicsDegenerate energy levelsBoundary (topology)Mathematical analysisObservabilityDegeneracy (biology)Boundary value problemWave equationSingularityApplied mathematicsPhysicsBiologyQuantum mechanicsBioinformaticsStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringAdvanced Mathematical Physics Problems