Stability of Non-Isolated Asymptotic Profiles for Fast Diffusion

The stability of asymptotic profiles of solutions to the Cauchy–Dirichlet problem for fast diffusion equation (FDE, for short) is discussed. The main result of the present paper is the stability of any asymptotic profiles of least energy. It is noteworthy that this result can cover non-isolated profiles, e.g., those for thin annular domain cases. The method of proof is based on the ?ojasiewicz–Simon inequality, which is usually used to prove the convergence of solutions to prescribed limits, as well as a uniform extinction estimate for solutions to FDE. Besides, local minimizers of an energy functional associated with this issue are characterized. Furthermore, the instability of positive radial asymptotic profiles in thin annular domains is also proved by applying the ?ojasiewicz–Simon inequality in a different way.     

Doubly nonlinear evolution equations with non-monotone perturbations

The local (in time) existence of strong solutions to Cauchy problems for doubly nonlinear abstract evolution equations with non-monotone perturbations in reflexive Banach spaces is proved under appropriate assumptions, which allow the case where solutions of the corresponding unperturbed problem may not be unique. To prove the existence, a couple of approximate problems are introduced and delicate limiting procedures are discussed by using various tools from convex analysis and the Kakutani-Ky Fan fixed point theorem. Furthermore, an application of the preceding abstract theory to a nonlinear PDE is also given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

FTIR investigation of the structure of vanadium oxides on ZrO2 and oxidation of toluene on it

The oxidation of toluene has been studied on V₂O₅/ZrO₂ by both FTIR spectroscopy and pulse method. The results suggest that Lewis-acidic sites play a significant role in the formation of benzaldehyde from toluene.

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Trace analysis of explosives in soil: pressurized fluid extraction and gas and liquid chromatography-mass spectrometry

Soil samples are collected from the former Open Burn/Open Detonation Unit, Makua Military Reservation, on the island of Oahu, Hawaii. The soil is the Helemano series. The soil samples are fortified with eight explosives for development of the analytical method. These analytes are 2-amino-4,6-dinitrotoluene; 1,3-dinitrobenzene; 2,4-dinitrotoluene (DNT); hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX); nitrobenzene (NB); octogen; 1,3,5-trinitrobenzene; and 2,4,6-trinitrotoluene. The analytes are recovered with pressurized fluid extraction and measured with liquid chromatography (LC), LC-mass spectrometry (MS), and gas chromatography-MS. Average recoveries of the seven analytes, except for NB, range from 67% to 110% from freshly fortified samples. The procedure fails to extract NB in soil. The average recoveries decrease from 67-110% to 41-81% as the soil is aged for 1 day to 6 months after fortification of the soil with the seven explosives. The field samples are analyzed for the presence of explosives, of which DNT and RDX are indeed detected. The results obtained with this procedure agree well with those obtained by an independent laboratory following the standard U.S. Environmental Protection Agency (EPA) method SW-846 8330. Compared with the EPA method, this new method provides MS confirmation of the analytes, and the extraction requires approximately 15 min, rather than 18 h by the EPA method.