Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions
El Mustapha Ait Ben Hassi, S. E. Chorfi, Lahcen Maniar
Abstract
Abstract In this work, we study the stable determination of four space-dependent coefficients appearing in a coupled semilinear parabolic system with variable diffusion matrices subject to dynamic boundary conditions which couple intern-boundary phenomena. We prove a Lipschitz stability result for interior and boundary potentials by means of only one observation component, localized in any arbitrary open subset of the physical domain. The proof mainly relies on some new Carleman estimates for dynamic boundary conditions of surface diffusion type.
Topics & Concepts
MathematicsLipschitz continuityBoundary (topology)Mathematical analysisStability (learning theory)Domain (mathematical analysis)Work (physics)Boundary value problemSpace (punctuation)DiffusionComponent (thermodynamics)Robin boundary conditionParabolic partial differential equationMixed boundary conditionPartial differential equationThermodynamicsPhysicsComputer sciencePhilosophyLinguisticsMachine learningAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problemsStability and Controllability of Differential Equations