Quantitative approximation properties for the fractional heat equation

By Angkana Rüland, Mikko Salo. Mathematical Control and Related Fields, 2017

55 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b29e563a7ef32b94ef35ed3d610259ea111ec8b6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems (2020, background): “xtend to the higher order cases? (6)Is there uniqueness for the conductivity type fractional Calderon problems [9, 13] in the higher order cases? (7)Could recent results on fractional heat equations [47, 69] be generalized to the higher order cases? (8)Does the higher regularity Runge approximation ”
The higher order fractional Calderón problem for linear local operators: Uniqueness (2020, background): “Other variants of the fractional Calderón problem include semilinear fractional (magnetic) Schrödinger equation [19, 20, 24, 25], fractional heat equation [21, 35] and fractional conductivity equation [8] (see also [6, 13] for equations arising from a nonlocal Schrödinger-type elliptic operator).”