Influence of damping on hyperbolic equations with parabolic degeneracy

This paper examines the effect of damping on a nonstrictly hyperbolic 2 x 2 system. It is shown that the growth of singularities is not restricted as in the strictly hyperbolic case where dissipation can be strong enough to preserve the smoothness of solutions globally in time. Here, irrespective of the stabilizing properties of damping, solutions are found to break down in finite time on a line where two eigenvalues coincide in state space

Formation of singularities for a class of nonlinear, hyperbolically degenerate initial-boundary value problems

AbstractWe examine a class of initial-boundary value problems of vector-valued solutions defined over a bounded domain in Rn. The presence of degeneracy in this class leads to loss of hyperbolicity at the null solution which gives rise to breakdown on the boundary of the domain when Dirichlet boundary conditions are imposed. Although the equations are set in an arbitrary number of spatial dimensions, it is possible to predict a maximal interval of existence for C1-solutions in this setting. A simple application to one-dimensional elasticity is also shown

Phase transitions and change of type in low-temperature heat

Classical heat pulse experiments have shown heat to propagate in waves through crystalline materials at temperatures close to absolute zero. With increasing temperature, these waves slow down and finally disappear, to be replaced by diffusive heat propagation. Several features surrounding this phenomenon are examined in this work. The model used switches between an internal parameter (or extended thermodynamics) description and a classical (linear or nonlinear) Fourier law setting. This leads to a hyperbolic-parabolic change of type, which allows wavelike features to appear beneath the transition temperature and diffusion above. We examine the region around and immediately below the transition temperature, where dissipative effects are insignificant

The Centaurus A Northern Middle Lobe as a Buoyant Bubble

We model the northern middle radio lobe of Centaurus A (NGC 5128) as a buoyant bubble of plasma deposited by an intermittently active jet. The extent of the rise of the bubble and its morphology imply that the ratio of its density to that of the surrounding ISM is less than 10^{-2}, consistent with our knowledge of extragalactic jets and minimal entrainment into the precursor radio lobe. Using the morphology of the lobe to date the beginning of its rise through the atmosphere of Centaurus A, we conclude that the bubble has been rising for approximately 140Myr. This time scale is consistent with that proposed by Quillen et al. (1993) for the settling of post-merger gas into the presently observed large scale disk in NGC 5128, suggesting a strong connection between the delayed re-establishment of radio emission and the merger of NGC 5128 with a small gas-rich galaxy. This suggests a connection, for radio galaxies in general, between mergers and the delayed onset of radio emission. In our model, the elongated X-ray emission region discovered by Feigelson et al. (1981), part of which coincides with the northern middle lobe, is thermal gas that originates from the ISM below the bubble and that has been uplifted and compressed. The "large-scale jet" appearing in the radio images of Morganti et al. (1999) may be the result of the same pressure gradients that cause the uplift of the thermal gas, acting on much lighter plasma, or may represent a jet that did not turn off completely when the northern middle lobe started to buoyantly rise. We propose that the adjacent emission line knots (the "outer filaments") and star-forming regions result from the disturbance, in particular the thermal trunk, caused by the bubble moving through the extended atmosphere of NGC 5128.Comment: 38 pages, 13 figures, submitted to ApJ; a version with higher resolution figures is available at http://www.mso.anu.edu.au/~saxton/papers/cena.pd