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It has been known since Lanford [19] that the dynamics of a hard sphere gas is described in the low density limit by the Boltzmann equation, at least for short times. The classical strategy of proof fails for longer times, even close to…

The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route ($\mu$…

In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in $B_{1,1}^{2} \times B_{1,1}^{1}$. This space of functions is a scale invariant subspace of $\dot{H}^{1/2} \times…

We consider a reaction-diffusion equation with a convection term in one space variable, where the diffusion changes sign from the positive to the negative and the reaction term is bistable. We study the existence of wavefront solutions,…

We study the asymptotic behavior of the solutions related to a family of singularly perturbed linear partial differential equations in the complex domain. The analytic solutions obtained by means of a Borel-Laplace summation procedure are…

Consider the planar restricted $(N+1)$-body problem with trajectories of the $N(\ge 2)$ primaries forming a collision-free periodic solution of the $N$-body problem, for any positive energy $h$ and directions $\theta_{\pm} \in [0, 2\pi)$,…

This paper is devoted to the proof of the existence of the principal eigenvalue and related eigenfunctions for fully nonlinear uniformly elliptic equations posed in a punctured ball, in presence of a singular potential. More precisely, we…

Highly spinning classical strings on RxS^3 are described by the Landau-Lifshitz model or equivalently by the Heisenberg ferromagnet in the thermodynamic limit. The spectrum of this model can be given in terms of spectral curves. However, it…

This paper study the two--phase problem for the forward-backward parabolic equation with diffusion function of cubic type. Existence and uniqueness for these kind of problems were obtained in literature in the case in which the phases are…

This paper is devoted to the study of travelling fronts of reaction-diffusion equations with periodic advection in the whole plane $\mathbb R^2$. We are interested in curved fronts satisfying some "conical" conditions at infinity. We prove…

We provide sufficient conditions for the existence of periodic solutions of the planar perturbed double pendulum with small oscillations.

The authors of the paper "The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom" [1] claim that they have derived the full third order perturbed KdV equation for the case of uneven bottom. We…

We prove recursive formulas for $\tau_d$, the number of degree $d$ elliptic curves with fixed j-invariant in P^n. We use analysis to relate the classical invariant $\tau_d$ to the genus one perturbed invariant $RT_{1,d}$ defined recently by…

G-equation is a popular level set model in turbulent combustion, and becomes an advective mean curvature type evolution equation when curvature of a moving flame in a fluid flow is considered: $$ G_t + \left(1-d\,…

We show that the XY quantum chain in a magnetic field is invariant under a two parameter deformation of the $SU(1/1)$ superalgebra. One is led to an extension of the braid group and the Hecke algebras which reduce to the known ones when the…

We give an exact solution of the $5D$ Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and…

For a small disk D centered at the origin in R^2, a smooth real-valued function S(x,y) on D, and a positive epsilon, we consider the measure of the points in D where |S(x,y)| < epsilon, as well as oscillatory integral analogues.…

Multidimensional contractions of irreducible representations of the Cayley-Klein unitary algebras in the Gel'fand-Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method…

We show in this letter that the perturbed Burgers equation $u_t = 2uu_x + u_{xx} + \epsilon ( 3 \alpha_1 u^2 u_x + 3\alpha_2 uu_{xx} + 3\alpha_3 u_x^2 + \alpha_4 u_{xxx} )$ is equivalent, through a near-identity transformation and up to…

We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution $u(x,t)$, the graph…