Waves of maximal height for a class of nonlocal equations with homogeneous symbols

We discuss the existence and regularity of periodic traveling-wave solutions of a class of nonlocal equations with homogeneous symbol of order $-r$, where $r>1$. Based on the properties of the nonlocal convolution operator, we apply analytic bifurcation theory and show that a highest, peaked, periodic traveling-wave solution is reached as the limiting case at the end of the main bifurcation curve. The regularity of the highest wave is proved to be exactly Lipschitz. As an application of our analysis, we reformulate the steady reduced Ostrovsky equation in a nonlocal form in terms of a Fourier multiplier operator with symbol $m(k)=k^{-2}$. Thereby we recover its unique highest $2\pi$-periodic, peaked traveling-wave solution, having the property of being exactly Lipschitz at the crest.Comment: 25 page

Creative Europe 2014-2020: A New Programme - A New Cultural Policy As Well?

In 2011 the European Commission developed a proposal for a regulation for the new framework programme for the cultural and creative sector for the 2014-2020 Financial Framework. The present programmes "Culture" (2007-2013), MEDIA for the audio-visual sector (2007-2013), and MEDIA Mundus for cooperation with professionals from third countries in the audio-visual area (2011-2013) are thereby to be brought together under a common framework and a new facility for providing financing (guarantee fund) is to be created. This study provides an overview of central changes in cultural support beginning in 2014, discusses the positions of the European Council and the European Parliament concerning the Commission's proposal, and presents criticisms put forth by civil-society stakeholders and members of the public. For this purpose, publicly stated positions and newspaper opinion pieces have been examined in an analysis of content and discourse, and individual voices from civil society have been surveyed via semi-structured interviews. Central points of criticism from the public, civil society and the European Parliament are, among others, the economic style of the programme, with its emphasis on competition, employment and the strategic development of audiences. Furthermore, the idea of culture in the new programme has been criticised, since it describes culture solely as a good and service, and the non-commercial value of culture is not expressed

Symmetry of periodic waves for nonlocal dispersive equations

Of concern is the $\textit{a priori}$ symmetry of traveling wave solutions for a general class of nonlocal dispersive equations $$u_t + (u^2 + Lu)_x = 0,$$ where $L$ is a Fourier multiplier operator with symbol $m$. Our analysis includes both homogeneous and inhomogeneous symbols. We characterize a class of symbols m guaranteeing that periodic traveling wave solutions are symmetric under a mild assumption on the wave profile. Particularly, instead of considering waves with a unique crest and trough per period or a monotone structure near troughs as classically imposed in the water wave problem, we formulate a $\textit{reflection criterion}$, which allows to affirm the symmetry of periodic traveling waves. The reflection criterion weakens the assumption of monotonicity between trough and crest and enables to treat $\textit{a priori}$ solutions with multiple crests of different sizes per period. Moreover, our result not only applies to smooth solutions, but also to traveling waves with a non-smooth structure such as peaks or cusps at a crest. The proof relies on a so-called $\textit{touching lemma}$, which is related to a strong maximum principle for elliptic operators, and a weak form of the celebrated $\textit{method of moving planes}$

Existence, regularity, and symmetry of periodic traveling waves for Gardner-Ostrovsky type equations

We study the existence, regularity, and symmetry of periodic traveling solutions to a class of Gardner-Ostrovsky type equations, including the classical Gardner-Ostrovsky equation, the (modified) Ostrovsky, and the reduced (modified) Ostrovsky equation. The modified Ostrovsky equation is also known as the short pulse equation. The Gardner-Ostrovsky equation is a model for internal ocean waves of large amplitude. We prove the existence of nontrivial, periodic traveling wave solutions using local bifurcation theory, where the wave speed serves as the bifurcation parameter. Moreover, we give a regularity analysis for periodic traveling solutions in the presence as well as absence of Boussinesq dispersion. We see that the presence of Boussinesq dispersion implies smoothness of periodic traveling wave solutions, while its absence may lead to singularities in the form of peaks or cusps. Eventually, we study the symmetry of periodic traveling solutions by the method of moving planes. A novel feature of the symmetry results in the absence of Boussinesq dispersion is that we do not need to impose a traditional monotonicity condition or a recently developed reflection criterion on the wave profiles to prove the statement on the symmetry of periodic traveling waves

On a thin film model with insoluble surfactant

This paper studies the existence and asymptotic behavior of global weak solutions for a thin film equation with insoluble surfactant under the influence of gravitational, capillary, and van der Waals forces. We prove the existence of global weak solutions for medium sized initial data in large function spaces. Moreover, exponential decay towards the flat equilibrium state is established, where an estimate on the decay rate can be computed explicitly

CII, CI, and CO in the massive star forming region W3 Main

We have used the KOSMA 3m telescope to map the core 7'x5' of the Galactic massive star forming region W3Main in the two fine structure lines of atomic carbon and four mid-J transitions of CO and 13CO. In combination with a map of singly ionized carbon (Howe et al. 1991), and FIR fine structure line data observed by ISO/LWS at the center position, these data sets allow to study in detail the physical structure of the photon dominated cloud interface regions (PDRs) where the occurance of carbon changes from CII to CI, and to CO.Comment: 4 pages, 4 figures, to appear in "Proceedings of the 4th Cologne-Bonn-Zermatt-Symposium, The dense interstellar medium in galaxies", eds. S. Pfalzner, C. Kramer, C. Straubmeier, and A. Heithausen (Springer Verlag