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RESEARCH PRODUCT
Quantitative Approximation Properties for the Fractional Heat Equation
Mikko SaloAngkana Rülandsubject
osittaisdifferentiaaliyhtälöt0209 industrial biotechnologyClass (set theory)Control and Optimizationfractional parabolic Calderón problemPseudodifferential operatorsApplied Mathematics010102 general mathematics02 engineering and technologyType (model theory)nonlocal operators [cost of approximation]01 natural sciencesinversio-ongelmatControllabilityMathematics - Analysis of PDEsweak unique continuation [Runge approximation]020901 industrial engineering & automationFOS: MathematicsApplied mathematicsHeat equationapproksimointi0101 mathematicsMathematicsAnalysis of PDEs (math.AP)description
In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal} pseudodifferential operators, we study quantitative approximation properties of solutions to it. First, relying on Runge type arguments, we give an alternative proof of certain \emph{qualitative} approximation results from \cite{DSV16}. Using propagation of smallness arguments, we then provide bounds on the \emph{cost} of approximate controllability and thus quantify the approximation properties of solutions to the fractional heat equation. Finally, we discuss generalizations of these results to a larger class of operators involving both local and nonlocal contributions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-08-21 |