This paper is devoted to the Cauchy problem for a class of doubly degenerate parabolic equation with time-dependent gradient source, where the initial data are Radon measures. Using the delicate a priori estimates, we first establish two local existence results. Furthermore, we show that the existence of solutions is optimal in the class considered here.
Introduction: The initial velocity of gas diffusion (ΔP) of coal is an important index to characterize the outburst risk of coal, and temperature is an important factor affecting the determination of initial velocity of gas diffusion. However, how to control the temperature during ΔP determination remains a significant challenge. Methods: In this paper, an experimental system for ΔP testing under temperature-controlled conditions was constructed, and the effect of temperature on the ΔP determination results was further explored by accurately controlling the temperature of the testing system. Results: The results show that the temperature change will affect the determination result of ΔP in the range of 13°C–40°C, and the determination results do not show obvious regularity. Discussion: The main reasons for the analysis are as follows: during the determination of ΔP, although the higher the temperature is, the faster the speed of gas diffusion and the greater the amount of gas diffusion and the pressure produced in the first 60 s, but the smaller the amount of gas adsorption before release. There is a situation of mutual offset between the two, resulting in the fluctuation of ΔP determination results. It is concluded that the temperature change will affect the determination of the initial velocity of gas diffusion, and when ΔP is measured, the temperature of the experimental system should be consistent with the actual temperature of the sampled coal body as far as possible, so as to increase the reliability of the measured results for the prediction of coal and gas outburst. This paper provides an experimental basis for clarifying the industry standard of temperature related to ΔP.
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