On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-

Multiple solutions for a class of perturbed second-order differential equations with impulses

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Perturbed nonlocal fourth order equations of Kirchhoff type with Navier boundary conditions

Abstract We investigate the existence of multiple solutions for perturbed nonlocal fourth-order equations of Kirchhoff type under Navier boundary conditions. We give some new criteria for guaranteeing that the perturbed fourth-order equations of Kirchhoff type have at least three weak solutions by using a variational method and some critical point theorems due to Ricceri. We extend and improve some recent results. Finally, by presenting two examples, we ensure the applicability of our results

Noble gas and carbon isotope systematics at the seemingly inactive Ciomadul volcano (Eastern‐Central Europe, Romania): evidence for volcanic degassing

Ciomadul is the youngest volcano in the Carpathian-Pannonian Region, Eastern-Central Europe, which last erupted 30 ka. This volcano is considered to be inactive, however, combined evidence from petrologic and magnetotelluric data, as well as seismic tomography studies suggest the existence of a subvolcanic crystal mush with variable melt content. The volcanic area is characterized by high CO2 gas output rate, with a minimum of 8.7 × 103 t yr-1. We investigated 31 gas emissions at Ciomadul to constrain the origin of the volatiles. The δ13C-CO2 and 3He/4He compositions suggest the outgassing of a significant component of mantle-derived fluids. The He isotope signature in the outgassing fluids (up to 3.10 Ra) is lower than the values in the peridotite xenoliths of the nearby alkaline basalt volcanic field (R/Ra 5.95Ra±0.01) which are representative of a continental lithospheric mantle and significantly lower than MORB values. Considering the chemical characteristics of the Ciomadul dacite, including trace element and Sr- Nd and O isotope compositions, an upper crustal contamination is less probable, whereas the primary magmas could have been derived from an enriched mantle source. The low He isotopic ratios could indicate a strongly metasomatized mantle lithosphere. This could be due to infiltration of subduction-related fluids and postmetasomatic ingrowth of radiogenic He. The metasomatic fluids are inferred to have contained subducted carbonate material resulting in a heavier carbon isotope composition (13C is in the range of -1.4 to -4.6 ‰) and an increase of CO2/3He ratio. Our study shows the magmatic contribution to the emitted gases

Urban electrical vehicles as the solution for public transportation in the cities of Romania

This paper shows that the European Recommendation COM (2007) 551 final finds that over 60% of the population lives in urban areas in the European Union (EU). Urban areas now constitute the living environment of the majority of the population and increased traffic in town and city centers has resulted in chronic congestion. Every year nearly 100 billion Euros, or 1% of the EU’s gross domestic product (GDP), are lost to the European economy as a result of this congestion. The analysis of the means of transport presented in this paper will show which electrical vehicle is the solution for non-polluting transport according to each specific need. The Romanian company ICPE SAERP, together with the Urban Transport Administration of Bucharest (RAT Bucharest), has modernized classic tramcars, equipping them with three-phase inverters and asynchronous motors and a partially lowered floor. By 2011, 18 tramcars will be modernized. ICPE SAERP together with ASTRA BUS Arad, will produce and deliver new trolleybuses with lowered floors in Bucharest. These new trolleybuses will be equipped with three-phase inverters, with asynchronous motors and with converters for the auxiliary services and for the air conditioning system. Also the trolleybus has a protection device against high voltage present on the body of the vehicle, which is controlled by means of a DSP processor in the master controller. The methodology used in the authors research is presented in this paper as well as the results that led to the conclusion that the type of public transportation proposed is cleaner, more reliable, more efficient and more comfortable than others