ﻻ يوجد ملخص باللغة العربية
We prove sharp pointwise decay estimates for critical Dirac equations on $mathbb{R}^n$ with $ngeq 2$. They appear for instance in the study of critical Dirac equations on compact spin manifolds, describing blow-up profiles, and as effective equations in honeycomb structures. For the latter case, we find excited states with an explicit asymptotic behavior. Moreover, we provide some classification results both for ground states and for excited states.
Sharp temporal decay estimates are established for the gradient and time derivative of solutions to a viscous Hamilton-Jacobi equation as well the associated Hamilton-Jacobi equation. Special care is given to the dependence of the estimates on the vi
We are concerned with the short- and large-time behavior of the $L^2$-propagator norm of Fokker-Planck equations with linear drift, i.e. $partial_t f=mathrm{div}_{x}{(D abla_x f+Cxf)}$. With a coordinate transformation these equations can be normali
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Dirac equation. To this end we develop basic scattering theory and establish a limiting absorption principle for discrete perturbed Dirac operators.
In this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by $e^{itphi(sqrt{-Delta})}$, where $phi: mathbb{R}^+to mathbb{R}$ is smooth away from the origin. Especially, the decay estimates for the soluti
We prove the existence of infinitely many non square-integrable stationary solutions for a family of massless Dirac equations in 2D. They appear as effective equations in two dimensional honeycomb structures. We give a direct existence proof thanks t