Search results for "Arabo"

Similaritons in optical fiber Raman amplifiers

2005

This thesis presents the generation of optical similaritons in a normally dispersive Raman amplifier at telecom wavelengths. The pulses experimentally characterized by FROG technique exhibit a parabolic intensity profile with a linear chirp, in good agreement with results of numerical simulations.Several theoretical features of the similaritons have been experimentally studied. The dynamics of two similaritons with same or different central wavelengths is also investigated: similaritons are robust against collisions, whereas the interaction of similaritons leads to the generation of high-repetition rate dark soliton train.The similariton properties have been finally applied into three field…

Coordinates for quasi-Fuchsian punctured torus space

1998

We consider complex Fenchel-Nielsen coordinates on the quasi-Fuchsian space of punctured tori. These coordinates arise from a generalisation of Kra's plumbing construction and are related to earthquakes on Teichmueller space. They also allow us to interpolate between two coordinate systems on Teichmueller space, namely the classical Fuchsian space with Fenchel-Nielsen coordinates and the Maskit embedding. We also show how they relate to the pleating coordinates of Keen and Series.

Existence and uniqueness for a degenerate parabolic equation with 𝐿¹-data

1999

In this paper we study existence and uniqueness of solutions for the boundary-value problem, with initial datum in L 1 ( Ω ) L^{1}(\Omega ) , u t = d i v a ( x , D u ) in  ( 0 , ∞ ) × Ω , \begin{equation*}u_{t} = \mathrm {div} \mathbf {a} (x,Du) \quad \text {in } (0, \infty ) \times \Omega , \end{equation*} − ∂ u ∂ η a ∈ β ( u ) on  ( 0 , ∞ ) × ∂ Ω , \begin{equation*}-{\frac {{\partial u} }{{\partial \eta _{a}}}} \in \beta (u) \quad \text {on } (0, \infty ) \times \partial \Omega ,\end{equation*} u ( x , 0 ) = u 0 ( x ) in  Ω , \begin{equation*}u(x, 0) = u_{0}(x) \quad \text {in }\Omega ,\end{equation*} where a is a Carathéodory function satisfying the classical Leray-Lions hypothesis, ∂ / …

Removability theorems for solutions of degenerate elliptic partial differential equations

1993

New special function recurrences giving new indefinite integrals

2018

ABSTRACTSequences of new recurrence relations are presented for Bessel functions, parabolic cylinder functions and associated Legendre functions. The sequences correspond to values of an integer variable r and are generalizations of each conventional recurrence relation, which correspond to r=1. The sequences can be extended indefinitely, though the relations become progressively more intricate as r increases. These relations all have the form of a first-order linear inhomogeneous differential equation, which can be solved by an integrating factor. This gives a very general indefinite integral for each recurrence. The method can be applied to other special functions which have conventional …

Existence results for $L^1$ data of some quasi-linear parabolic problems with a quadratic gradient term and source

2002

In this paper we deal with a Cauchy–Dirichlet quasilinear parabolic problem containing a gradient lower order term; namely, ut - Δu + |u|2 γ-2u |∇u|2 = |u|p-2u. We prove that if p ≥ 1, γ ≥ ½ and p < 2 γ + 2, then there exists a global weak solution for all initial data in L1 (Ω). We also see that there exists a non-negative solution if the initial datum is non-negative.

Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term

2006

We study existence and regularity of distributional solutions for possibly degenerate quasi-linear parabolic problems having a first order term which grows quadratically in the gradient. The model problem we refer to is the following (1){ut−div(α(u)∇u)=β(u)|∇u|2+f(x,t),in Ω×]0,T[;u(x,t)=0,on ∂Ω×]0,T[;u(x,0)=u0(x),in Ω. Here Ω is a bounded open set in RN, T>0. The unknown function u=u(x,t) depends on x∈Ω and t∈]0,T[. The symbol ∇u denotes the gradient of u with respect to x. The real functions α, β are continuous; moreover α is positive, bounded and may vanish at ±∞. As far as the data are concerned, we require the following assumptions: ∫ΩΦ(u0(x))dx<∞ where Φ is a convenient function which …

Classification criteria for regular trees

2021

Esitämme säännöllisten puiden parabolisuudelle yhtäpitäviä ehtoja. We give characterizations for the parabolicity of regular trees. peerReviewed

A relation between the curvature ellipse and the curvature parabola

2019

Abstract At each point in an immersed surface in ℝ4 there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. Recently, at the singular point of a corank 1 singular surface in ℝ3, a curvature parabola in the normal plane which codifies all the local second order geometry has been defined. When projecting a regular surface in ℝ4 to ℝ3 in a tangent direction, corank 1 singularities appear generically. The projection has a cross-cap singularity unless the direction of projection is asymptotic, where more degenerate singularities can appear. In this paper we relate the geometry of an immersed surface in ℝ4 at a certain point to the geome…

Renormalized solutions for degenerate elliptic–parabolic problems with nonlinear dynamical boundary conditions and L1-data

2008

Abstract We consider a degenerate elliptic–parabolic problem with nonlinear dynamical boundary conditions. Assuming L 1 -data, we prove existence and uniqueness in the framework of renormalized solutions. Particular instances of this problem appear in various phenomena with changes of phase like multiphase Stefan problems and in the weak formulation of the mathematical model of the so-called Hele–Shaw problem. Also, the problem with non-homogeneous Neumann boundary condition is included.