Allahverdi N., Pozo A., Zuazua E. Numerical aspects of sonic-boom minimization COMMUN CONTEMP MATH. Vol. No. 658 (2016), pp. 267 – 279. DOI: 10.1090/conm/658/13133
Abstract: The propagation of the sonic-boom produced by supersonic aircrafts can be modeled by means of a nonlocal version of the viscous Burgers equation. In this paper, motivated by the sonic-boom minimization problem, we analyze the numerical aspects of the optimization process, with a focus on the large-time dynamics of the underlying model. We develop an adjoint methodology at the numerical level allowing to recover accurate approximations of the minimizers. We observe however that some of the minima are hard to achieve due to the intrinsic nonlinear and viscous effects.