Persistence and unique continuation principles in weighted spaces for solutions of the fractional Korteweg- de Vries equation.

Abstract: Persistence problems in weighted spaces have been studied for differ- ent dispersive models involving non-local operators. Generally, these equations do not propagate polynomial weights of arbitrary magni- tude, and the maximum decay rate is associated with the dispersive part of the equation. Altogether, this analysis is complemented by unique continuation principles that determine optimal spatial decay. This talk aims to show our results on the preceding questions for a weakly dispersive perturbation of the inviscid Burgers equation, which comprises the Burgers-Hilbert equation and dispersive effects weaker than those of the Benjamin-ono equation.

Posted on Jul 3, 2021 in Differential Equations, Seminars