Here u(x, t) represents the free surface of the liquid and the parameter γ > 0 measures the effect of rotation. (1.1) describes the propagation of internal waves of even modes in the ocean; for instance, see the work of Galkin and Stepanyants [1], Leonov [2], and Shrira [3, 4]. The parameter β determines the type of dispersion, more precisely, when β < 0, (1.1) denotes the generalized Ostrovsky...

Zero modes of rotationally symmetric vortices in a hierarchy of generalized Abelian Higgs models are studied. Under the finite-energy and the smoothness condition, it is shown, that in all models, n self-dual vortices superimposed at the origin have 2n modes. The relevance of these modes for vortex scattering is discussed, first in the context of the slow-motion approximation. Then a correspond...

Well-posedness of the Cauchy problem is analyzed for a singular Vlasov equation governing the evolution of the ionic distribution function of a quasineutral fusion plasma. The Penrose criterium is adapted to the linearized problem around a time and space homogeneous distribution function showing (due to the singularity) more drastic differences between stable and unstable situations. This patho...

Bibliography 75 Index 77 v Introduction Evolution means the change of a certain system with respect to time. In a more suggestive language, one could talk of the " motion " of a system in time. Examples could be the movement of planets, the growth of a population, ... From a philosophical point of view (cf. G. Nickel in [9]) it turns out, that the right mathematical model for evolution is a one...

We consider the Cauchy problem for the one-dimensional PeronaMalik equation ut = 1− ux (1 + ux) 2 uxx in the interval [−1, 1], with homogeneous Neumann boundary conditions. We prove that the set of initial data for which this equation has a localin-time classical solution u : [−1, 1]× [0, T ] → R is dense in C1([−1, 1]). Here “classical solution” means that u, ut, ux and uxx are continuous func...