Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation
María Ángeles García‐Ferrero, Angkana Rüland, Wiktoria Zatoń
Abstract
<p style='text-indent:20px;'>In this article, we discuss quantitative Runge approximation properties for the acoustic Helmholtz equation and prove stability improvement results in the high frequency limit for an associated partial data inverse problem modelled on [<xref ref-type="bibr" rid="b3">3</xref>,<xref ref-type="bibr" rid="b35">35</xref>]. The results rely on quantitative unique continuation estimates in suitable function spaces with explicit frequency dependence. We contrast the frequency dependence of interior Runge approximation results from non-convex and convex sets.</p>
Topics & Concepts
MathematicsStability (learning theory)Helmholtz equationRegular polygonHelmholtz free energyMathematical analysisInverseContinuationFunction (biology)Convex functionApplied mathematicsPhysicsGeometryComputer scienceThermodynamicsBoundary value problemProgramming languageBiologyEvolutionary biologyMachine learningNumerical methods in inverse problemsAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential Equations