This paper is concerned with a chemotaxis system with singular sensitivity and logistic source,under the homogeneous Neumann boundary conditions and for widely arbitrary positive initial data in a bounded domain Ω ⊂ R n (n ≥ 1) with smooth boundary, where χ i , μ i > 0 (i = 1, 2) and α, β > 1. It is proved that there exists a global classical solution if max{χ 1 , χ 2 } < 2 n , min{μ 1 , μ 2 } > n-2 n , α = β = 2 for n ≥ 2 or any χ i > 0 (i = 1, 2), μ i > 0 (i = 1, 2), α, β > 1 for n = 1.
MSC: 35K55; 35Q92
A prototype thermocompressor driven by linear motor was setup and experimental tudied. Peak-peak pressure in the system was influenced by the regenerator, the heating temperature and the gap clearance between piston and cylinder. The optimal frequency of the system was determined by spring constant and total mass of piston, shaft and moving iron. The peak-peak pressure was found to change little with filling pressure when the heating temperature was lower than 250°C, employing with N2 or He4 as the working substance. But when the heating temperature was higher than 250°C, peak-peak pressure increased with filling pressure. Besides, Helium4 was found to perform better than Nitrogen as the working substance. For heating temperature of 650°C and cooling temperature of 40°C, the peak-peak pressure could reach 0.412MPa with pressure ratio of 1.13 when the filling pressure was 2.2MPa, which could be used to drive the pulse tube crycooler (PTC).
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