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Equilibrium analysis for a mass-conserving model in presence of cavitation
Affiliation:1. R&D center, Nihon Densan Corporation, Tainan City 70955, Taiwan;2. Department of Mechanical Engineering and Advanced Institute of Manufacturing with High-tech Innovations, National Chung Cheng University, Chia-yi County 62102, Taiwan;3. Research & Development Section, Tung Pei industrial co. ltd., Taoyuan City 33420, Taiwan;4. Department of Mechanical Engineering, National Central University, Taoyuan City 32001, Taiwan;1. Royal Observatory of Belgium, Seismology and Gravimetry Department, Avenue Circulaire 3, B-1180 Brussels, Belgium;2. Belgian National Agency for Radioactive Waste and Enriched Fissile Material (ONDRAF/NIRAS), Long-term Research, Design & Development Department, Avenue des Arts 14, B-1210 Brussels, Belgium;3. Ghent University, Faculty of Sciences, Department of Geology, Laboratory of Mineralogy and Petrology, Krijgslaan 281 (S8), B-9000 Ghent, Belgium;4. Belgian Nuclear Research Centre (SCK•CEN), Institute for Environment, Health and Safety, Boeretang 200, B-2400 Mol, Belgium;5. Samsuffit-Geoservices BVBA, Eggelstraat 8, B-2530 Boechout, Belgium;6. University of Cologne, Institute of Geography, Albertus-Magnus-Platz, 50923 Cologne, Germany;7. Royal Museum for Central Africa, Earth Sciences, Surface Environments and Collection Management, Leuvensesteenweg 13, B-3080 Tervuren, Belgium;8. KULeuven, Department of Earth and Environmental Sciences, Division of Geology, Celestijnenlaan 200 E, B-3001 Heverlee, Belgium
Abstract:We study the existence of equilibrium positions for the load problem in Lubrication Theory. The problem consists of two surfaces in relative motion separated by a small distance filled by a lubricant. The system is described by the modified Reynolds equation (Elrod–Adams model) which describes the behavior of the lubricant and an extra integral equation given the balance of forces. The balance of forces allows to obtain the unknown position of the surfaces, defined with one degree of freedom.
Keywords:Reynolds lubrication equation  Inverse problems  Weighted Sobolev spaces  Singular perturbation analysis  Maximum principle
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