An Inverse Boundary Value Problem for a Semilinear Wave Equation on Lorentzian Manifolds
Peter Hintz, Günther Uhlmann, Jian Zhai
Abstract
Abstract We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the knowledge of the Neumann-to-Dirichlet map. Either distorted plane waves or Gaussian beams can be used to derive uniqueness.
Topics & Concepts
MathematicsMathematical analysisUniquenessWave equationManifold (fluid mechanics)Boundary value problemInverseNeumann boundary conditionBoundary (topology)Inverse problemDirichlet distributionGeometryMechanical engineeringEngineeringNumerical methods in inverse problemsAdvanced Mathematical Modeling in EngineeringThermoelastic and Magnetoelastic Phenomena