相关论文: The zero-dispersion limit for the Benjamin--Ono eq…

We prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy [Spherical dispersion with an application to polygonal approximation of curves, Anz. \"Osterreich. Akad. Wiss.…

This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified…

The Artmann formula provides an accurate determination of the Goos-Haenchen lateral displacement in terms of the light wavelength, refractive index and incidence angle. In the total reflection region, this formula is widely used in the…

We derive a $L^1_x (\mathbb R^d)-L^{\infty}_x ( \mathbb R^d)$ decay estimate of order $\mathcal O \left( t^{-d/2}\right)$ for the linear propagators $$\exp \left( {\pm it \sqrt{ |D|\left(1+ \beta |D|^2\right) \tanh |D | } }\right), \qquad…

We consider the periodic dispersion generalized Benjamin-Ono equations with polynomial nonlinearity. We establish the nonlinear smoothing properties of these equations, according to which the difference between the solution and the linear…

The Blackstock-Crighton equation models nonlinear acoustic wave propagation in thermo-viscous fluids. In the present work we investigate the associated inhomogeneous Dirichlet and Neumann boundary value problems in a bounded domain and…

A Chernoff-type distribution is a nonnormal distribution defined by the slope at zero of the greatest convex minorant of a two-sided Brownian motion with a polynomial drift. While a Chernoff-type distribution is known to appear as the…

In this paper we study the zero-viscosity limit of $2$-D Boussinesq equations with vertical viscosity and zero diffusivity, which is a nonlinear system with partial dissipation arising in atmospheric sciences and oceanic circulation. The…

We study ultradistributional boundary values of zero solutions of a hypoelliptic constant coefficient partial differential operator $P(D) = P(D_x, D_t)$ on $\mathbb{R}^{d+1}$. Our work unifies and considerably extends various classical…

In this article, global stabilization results for the two dimensional (2D) viscous Burgers' equation, that is, convergence of unsteady solution to its constant steady state solution with any initial data, are established using a nonlinear…

Upper bounds for the $L_p$-discrepancies of point distributions in compact metric measure spaces for $0<p\le\infty$ have been established in the paper [6] by Brandolini, Chen, Colzani, Gigante and Travaglini. In the present paper we show…

This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…

We study a Sobolev critical fast diffusion equation in bounded domains with the Brezis-Nirenberg effect. We obtain extinction profiles of its positive solutions, and show that the convergence rates of the relative error in regular norms are…

In this paper we investigate the one dimensional (1D) logarithmic diffusion equation with nonlinear Robin boundary conditions, namely, \[ \left\{ \begin{array}{l} \partial_t u=\partial_{xx} \log u\quad \mbox{in}\quad \left[-l,l\right]\times…

This article addresses some asymptotic and numerical issues related to the solution of Burgers' equation, $-\epsilon u_{xx} + u_t + u u_x = 0$ on $(-1,1)$, subject to the boundary conditions $u(-1) = 1 + \delta$, $u(1) = -1$, and its…

We consider the semilinear diffusion equation $\partial$ t u = Au + |u| $\alpha$ u in the half-space R N + := R N --1 x (0, +$\infty$), where A is a linear diffusion operator, which may be the classical Laplace operator, or a fractional…

The $p$-widths of a closed Riemannian manifold are a nonlinear analogue of the spectrum of its Laplace--Beltrami operator, which corresponds to areas of a certain min-max sequence of possibly singular minimal submanifolds. We show that the…

We consider the $k$-dispersion generalized Benjamin-Ono ($k$-DGBO) equations. For nonlinearities with power $k \geq 4$, we establish local and global well-posedness results for the associated initial value problem (IVP) in both the critical…

We prove that for any $0 < s < 1/2$, the Benjamin--Ono equation on the torus is globally in time $C^0-$well-posed on the Sobolev space $H^{-s}(\T, \R)$,in the sense that the solution map, which is known to be defined for smooth data,…

We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the…