This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place onl...This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions.展开更多
Inspired by previous resistance models for porous media, a resistance expression of gas migration within coal seams based on the ideal matchstick geometry, combined with the Darcy equation and the modified Poiseuille ...Inspired by previous resistance models for porous media, a resistance expression of gas migration within coal seams based on the ideal matchstick geometry, combined with the Darcy equation and the modified Poiseuille equation is proposed. The resistance to gas migration is generally dynamic because of the variations in adsorption swelling and matrix shrinkage. Due to the limitations of experimental conditions,only a theoretical expression of resistance to gas migration in coal is deduced, and the impacts of tortuosity, effective stress and pore pressure on the resistance are then considered. To validate the proposed expression, previous data from other researchers are adopted for the history matching exercise, and the agreement between the two is good.展开更多
基金Supported by the Innovation Project for University Prominent Research Talents of Henan (2003KJCX008)
文摘This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions.
基金supported by the State Key Research Development Program of China (Nos. 2016YFC0801402 and 2016YFC0600708)the National Natural Science Foundation of China (No. 51474219)
文摘Inspired by previous resistance models for porous media, a resistance expression of gas migration within coal seams based on the ideal matchstick geometry, combined with the Darcy equation and the modified Poiseuille equation is proposed. The resistance to gas migration is generally dynamic because of the variations in adsorption swelling and matrix shrinkage. Due to the limitations of experimental conditions,only a theoretical expression of resistance to gas migration in coal is deduced, and the impacts of tortuosity, effective stress and pore pressure on the resistance are then considered. To validate the proposed expression, previous data from other researchers are adopted for the history matching exercise, and the agreement between the two is good.
