Schaeffer's regularity theorem for scalar conservation laws does not extend to systems

Several regularity results hold for the Cauchy problem involving one scalar conservation law having convex flux. Among these, Schaeffer's theorem guarantees that if the initial datum is smooth and is generic, in the Baire sense, the entropy admissible solution develops at most finitely many shocks, locally, and stays smooth out of them. We rule out with the present paper the possibility of extending Schaeffer's regularity result to the class of genuinely nonlinear, strictly hyperbolic systems of conservation laws. The analysis relies on careful interaction estimates and uses fine properties of the wave-front tracking approximation

Nanosized Sodium-Doped Lanthanum Manganites: Role of the Synthetic Route on their Physical Properties

In this paper we present the results of the synthesis and characterisation of nanocrystalline La1-xNaxMnO3+delta samples. Two synthetic routes were employed: polyacrylamide-based sol-gel and propellant synthesis. Pure, single phase materials were obtained with grain size around 35 nm for the sol-gel samples and around 55 nm for the propellant ones, which moreover present a more broaden grain size distribution. For both series a superparamagnetic behaviour was evidenced by means of magnetisation and EPR measurements with peculiar features ascribable to the different grain sizes and morphology. Preliminary magnetoresistivity measurements show enhanced low-field (< 1 T) magnetoresistance values which suggest an interesting applicative use of these manganites.Comment: 31 Pages 10 Figures to appear in Chem. Mate

An overview on the approximation of boundary Riemann problems through physical viscosity

This note aims at providing an overview of some recent results concerning the viscous approximation of so-called boundary Riemann problems for nonlinear systems of conservation laws in small total variation regimes. \ua9 2016, Sociedade Brasileira de Matem\ue1tica

Orientational Effects and Random Mixing in 1-Alkanol + Alkanone Mixtures

1-Alkanol + alkanone systems have been investigated through the data analysis of molar excess functions, enthalpies, isobaric heat capacities, volumes and entropies, and using the Flory model and the formalism of the concentrationconcentration structure factor (SCC(0)). The enthalpy of the hydroxyl-carbonyl interactions has been evaluated. These interactions are stronger in mixtures with shorter alcohols (methanol-1-butanol) and 2-propanone or 2-butanone. However, effects related to the self-association of alcohols and to solvation between unlike molecules are of minor importance when compared with those which arise from dipolar interactions. Physical interactions are more relevant in mixtures with longer 1-alkanols. The studied systems are characterized by large structural effects. The variation of the molar excess enthalpy with the alcohol size along systems with a given ketone or with the alkanone size in solutions with a given alcohol are discussed in terms of the different contributions to this excess function. Mixtures with methanol show rather large orientational effects. The random mixing hypothesis is attained to a large extent for mixtures with 1-alkanols ≠ methanol and 2-alkanones. Steric effects and cyclization lead to stronger orientational effects in mixtures with 3-pentanone, 4-heptanone, or cyclohexanone. The increase of temperature weakens orientational effects. Results from SCC(0) calculations show that homocoordination is predominant and support conclusions obtained from the Flory model.Ministerio de Ciencia e Innovación, under Project FIS2010-1695

New interaction estimates for the Baiti-Jenssen system

We establish new interaction estimates for a system introduced by Baiti and Jenssen. These estimates are pivotal to the analysis of the wave front-tracking approximation. In a companion paper we use them to construct a counter-example which shows that Schaeffer\u2019s Regularity Theorem for scalar conservation laws does not extend to systems. The counter-example we construct shows, furthermore, that a wave-pattern containing infinitely many shocks can be robust with respect to perturbations of the initial data. The proof of the interaction estimates is based on the explicit computation of the wave fan curves and on a perturbation argument