In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^...In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^(∞) weak-entropy solution converges to the nonlinear diffusion wave of the generalized porous media equation(GPME)in L^(2)(R).As λ∈(1/7,1),we prove that the L^(∞) weak-entropy solution converges to an expansion around the nonlinear diffusion wave in L^(2)(R),which is the best asymptotic profile.The proof is based on intensive entropy analysis and an energy method.展开更多
For preventing and extinguishing the spontaneous combustion of coal seam, based on the importance for sealing air leakage channels in roadway, developed a material of light-paste for coalmine, and research its ingredi...For preventing and extinguishing the spontaneous combustion of coal seam, based on the importance for sealing air leakage channels in roadway, developed a material of light-paste for coalmine, and research its ingredient, proportion and performance. The result indicates that the component ratio of the material is which PB exciting agent is 20%, complex reinforcing agent is 2%, complex expansion agent is 1%, and A-material is 77%. The performances of compressive strength, swelling ratio and expansion time are optimum. The light-paste material can effectively seal air leakage channels for preventing and extinguishing the spontaneous combustion of coal seam in coalmine.展开更多
In 2003, Gasser-Hsiao-Li [JDE(2003)] showed that the solution to the bipolar hydrodynamic model for semiconductors(HD model) without doping function time-asymptotically converges to the diffusion wave of the porous me...In 2003, Gasser-Hsiao-Li [JDE(2003)] showed that the solution to the bipolar hydrodynamic model for semiconductors(HD model) without doping function time-asymptotically converges to the diffusion wave of the porous media equation(PME) for the switch-off case. Motivated by the work of Huang-Wu[arXiv:2210.13157], we will confirm that the time-asymptotic expansion proposed by Geng-Huang-Jin-Wu [arXiv:2202.13385] around the diffusion wave is a better asymptotic profile for the HD model in this paper, where we mainly adopt the approximate Green function method and the energy method.展开更多
基金S.Geng's research was supported in part by the National Natural Science Foundation of China(12071397)Excellent Youth Project of Hunan Education Department(21B0165)+1 种基金F.Huang's research was supported in part by the National Key R&D Program of China 2021YFA1000800the National Natural Science Foundation of China(12288201).
文摘In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^(∞) weak-entropy solution converges to the nonlinear diffusion wave of the generalized porous media equation(GPME)in L^(2)(R).As λ∈(1/7,1),we prove that the L^(∞) weak-entropy solution converges to an expansion around the nonlinear diffusion wave in L^(2)(R),which is the best asymptotic profile.The proof is based on intensive entropy analysis and an energy method.
基金Supported by the National Natural Science Foundation of China （1097178） the Project of Creative Team by the Mimstry of Education of China （IRT0856） the Natural Science Foundation of the Education Department of Shaanxi Province （09JK590）
文摘For preventing and extinguishing the spontaneous combustion of coal seam, based on the importance for sealing air leakage channels in roadway, developed a material of light-paste for coalmine, and research its ingredient, proportion and performance. The result indicates that the component ratio of the material is which PB exciting agent is 20%, complex reinforcing agent is 2%, complex expansion agent is 1%, and A-material is 77%. The performances of compressive strength, swelling ratio and expansion time are optimum. The light-paste material can effectively seal air leakage channels for preventing and extinguishing the spontaneous combustion of coal seam in coalmine.
基金supported by the National Natural Science Foundation of China(No.12201649)。
文摘In 2003, Gasser-Hsiao-Li [JDE(2003)] showed that the solution to the bipolar hydrodynamic model for semiconductors(HD model) without doping function time-asymptotically converges to the diffusion wave of the porous media equation(PME) for the switch-off case. Motivated by the work of Huang-Wu[arXiv:2210.13157], we will confirm that the time-asymptotic expansion proposed by Geng-Huang-Jin-Wu [arXiv:2202.13385] around the diffusion wave is a better asymptotic profile for the HD model in this paper, where we mainly adopt the approximate Green function method and the energy method.
