In this paper we describe some analytical properties of the R1/m law proposed by Sersic (1968) to categorize the photometric profiles of elliptical galaxies. In particular, we present the full asymptotic expansion for the dimensionless scale factor b(m) that is introduced when referring the profile to the standard effective radius. Surprisingly, our asymptotic analysis turns out to be useful ev...

We consider variational problems defined on domains ‘weakly’ connected through a separation hyperplane (‘sieve plane’) by an ε-periodically distributed ‘contact zone’. We study the asymptotic behaviour as ε tends to 0 of integral functionals in such domains in the nonlinear and vector-valued case, showing that the asymptotic memory of the sieve is described by a nonlinear ‘capacitarytype’ formu...

In this paper, we give an alternative proof for the asymptotic stability of solitons nonlinear Schrödinger equations with internal modes. The novel idea is to use “refined profiles” developed by authors analysis small bound states. By new strategy, able avoid normal forms. Further, can track functions appearing in Fermi Golden Rule hypothesis.

The asymptotic profile for diffusion wave terms of solutions to the compressible Navier–Stokes–Korteweg system is studied on R2. with time-decay estimate was by Hoff and Zumbrun (1995, 1997), Kobayashi Shibata (2002), Tsuda (2018) Navier–Stokes systems. Our main assertion in this paper that, some initial conditions given Hardy space, behaviors space–time L2 parts are essentially different betwe...

<p style='text-indent:20px;'>We introduce a new model of the logarithmic type wave like plate equation with nonlocal damping mechanism. We consider Cauchy problem for this in <inline-formula><tex-math id="M1">\begin{document}$ {{\bf R}}^{n} $\end{document}</tex-math></inline-formula>, and study asymptotic profile optimal decay rates solutions as id="M2">\begin{d...

We consider the long time behavior of solutions to initial value problem for ``complex-valued'' cubic nonlinear Klein-Gordon equation (NLKG) in one space dimension. In [12], Sunagawa derived $L^{\infty}$ decay estimate (NLKG). this note, we obtain large asymptotic profile