An Inverse Problem for the Wave Equation with Nonlinear Dumping
V. G. Romanov
Abstract
We study the inverse problem of recovering a coefficient at the nonlinearity in a second order hyperbolic equation with nonlinear damping. The unknown coefficient depends on one space variable $ x $ . Also, we consider the process of wave propagation along the semiaxis $ x>0 $ given the derivative with respect to $ x $ at $ x=0 $ . As additional information in the inverse problem we consider the trace of a solution to the initial boundary value problem on a finite segment of the axis $ x=0 $ and find the conditions for unique solvability of the direct problem. We also establish a local existence theorem and a global stability estimate for a solution to the inverse problem.
Topics & Concepts
MathematicsInverse problemMathematical analysisHyperbolic partial differential equationNonlinear systemInverseWave equationBoundary value problemTRACE (psycholinguistics)Space (punctuation)Initial value problemApplied mathematicsPartial differential equationGeometryPhysicsLinguisticsQuantum mechanicsPhilosophyNumerical methods in inverse problemsStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in Engineering