On the asymptotic behavior for convection-diffusion equations associated to higher order elliptic operators in divergence form

We consider the linear convection-diffusion equation associated to higher order elliptic operators (ut + Ltu = aru on Rn × (0,1) u(0) = u0 2 L1(Rn), (1) where a is a constant vector in Rn, m 2 N_, n _ 1 and L0 belongs to a class of higher order elliptic operators in divergence form associated to non-smooth bounded measurable coefficients on Rn. The aim of this paper is to study the asymptotic behavior, in Lp (1 _ p _ 1), of the derivatives Du(t) of the solution of (1) when t tends to 1.We consider the linear convection-diffusion equation associated to higher order elliptic operators (ut + Ltu = aru on Rn × (0,1) u(0) = u0 2 L1(Rn), (1) where a is a constant vector in Rn, m 2 N_, n _ 1 and L0 belongs to a class of higher order elliptic operators in divergence form associated to non-smooth bounded measurable coefficients on Rn. The aim of this paper is to study the asymptotic behavior, in Lp (1 _ p _ 1), of the derivatives Du(t) of the solution of (1) when t tends to 1

Nonexistence results for the Cauchy problem for some fractional nonlinear systems of thermo-elasticity type

We study the nonexistence of global solutions to the Cauchy problem for systems of parabolic-hyperbolic or hyperbolic thermo-elasticity equations posed in RN. For power nonlinearities, we present threshold critical exponents depending on the space dimension N. Our method of proof rests on the nonlinear capacity method. 2016 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimThis publication was made possible by NPRP Grant NPRP 6?137?1?026 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.Scopu

Coupling of electrochemical techniques to study copper corrosion inhibition in 0.5 mol L-1 NaCl by 1-pyrrolidine dithiocarbamate

International audienceIn this work, as for the preliminary step to the protection of Al 2xxx alloys, the anticorrosion effect of environmentally friendly 1-pyrrolidine dithiocarbamate (PDTC) on Cu was investigated by combining various electrochemical methods in addition to SEM-EDS analyses and gravimetric measurements. The Cu/PDTC system was used as a model to simulate the inhibition of Cu-rich particles contained in Al 2xxx alloys. The corrosion test solution was 0.5 mol NaCl in the presence of 10(-4), 10(-3), or 10(-2) mol L-1 PDTC. The immersion time of the copper electrode was extended generally up to 24 h. By EQCM measurements, a marked protective effect of PDTC was observed for the highest PDTC used, and corroborated by voltammetry and EIS measurements. The cathodic reduction under constant current allowed determining the corrosion products remaining on the copper surface in terms of electrical charge. The protective effect of PDTC was explained by the formation of highly stable compounds on the copper surface, which decreases the rate of both anodic dissolution and oxygen reduction reaction

Cathodic behavior of pure Al in sulfate media

International audienceThe cathodic behavior of Al in 0.5 M Na2SO4 solution was studied by electrochemical methods. It was shown that the reduction of Fe(CN)63- was difficult when an oxide layer was formed on the electrode surface during 1 h immersion in 0.5 M Na2SO4 solution due to the poor ionic and electronic conductivities of Al hydroxides. This reaction required a high cathodic overpotential on Al surface pre-treated at –2 V/SCE Al and was kinetically more difficult in comparison to platinum. Rotating disk electrode measurements showed that oxygen reduction reaction (ORR) was controlled by kinetics on both Al pre-treated at –2 V/SCE and oxidized Al cathodic dissolution was controlled by the supply of OH– ions through H2 evolution and by ORR on both oxidized Al electrode and the Al surface pre-treated at –2 V/SCE. Polarization curves obtained at different pH values showed that no dissolution behavior was observed at pH 5, whereas in neutral and alkaline solutions, OH– ions production induced chemical dissolution of the hydroxide layer. In O2 supersaturated solution, it was shown that ORR kinetics were slightly favored

Effect of 1-pyrrolidine dithiocarbamate on the galvanic coupling resistance of intermetallics – Aluminum matrix during corrosion of AA 2024-T3 in a dilute NaCl

International audience1-pyrrolidine dithiocarbamate (PDTC) effect on galvanic coupling resistance of AA 2024-T3 alloy in0.2 g L1 NaCl was evaluated by different electrochemical/gravimetric methods and surface analysis.The results obtained from polarization curves and electrochemical quartz crystal microbalance measurementsshowed that PDTC forms an adsorbed film on the Cu-rich particles, likely through a CuI–PDTC complex.At high concentrations, PDTC significantly decreases the alloy reactivity thereby providing a markedcorrosion protection. SEM–EDX analysis showed that PDTC adsorbs preferentially on the Al–Cu–Mgparticles. Electrochemical impedance spectroscopy measurements corroborate these results and showfurthermore that PDTC addition increases the galvanic coupling resistance

Sensibilite du cuivre pur ou faiblement allie a la corrosion par piqures dans des solutions tampoins contenant des ions chlorures, sulfates ou nitrates

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : T 83373 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc