This paper considers a kind of strongly coupled cross diffusion parabolic system, which can be used as the multi-dimensional Lyurnkis energy transport model in semiconductor science. The global existence and large tim...This paper considers a kind of strongly coupled cross diffusion parabolic system, which can be used as the multi-dimensional Lyurnkis energy transport model in semiconductor science. The global existence and large time behavior are obtained for smooth solution to the initial boundary value problem. When the initial data are a small perturbation of an isothermal stationary solution, the smooth solution of the problem under the insulating boundary condition, converges to that stationary solution exponentially fast as time goes to infinity.展开更多
Cross-diffusion is a ubiquitous phenomenon in complex networks, but it is often neglected in the study of reaction–diffusion networks. In fact, network connections are often random. In this paper, we investigate patt...Cross-diffusion is a ubiquitous phenomenon in complex networks, but it is often neglected in the study of reaction–diffusion networks. In fact, network connections are often random. In this paper, we investigate pattern dynamics of random networks with cross-diffusion by using the method of network analysis and obtain a condition under which the network loses stability and Turing bifurcation occurs. In addition, we also derive the amplitude equation for the network and prove the stability of the amplitude equation which is also an effective tool to investigate pattern dynamics of the random network with cross diffusion. In the meantime, the pattern formation consistently matches the stability of the system and the amplitude equation is verified by simulations. A novel approach to the investigation of specific real systems was presented in this paper. Finally, the example and simulation used in this paper validate our theoretical results.展开更多
The purpose of this paper is to study the effect of cross diffusion in a competition model with stage structure, under homogeneous Neumann boundary condition. It will be shown that cross diffusion cannot only destabil...The purpose of this paper is to study the effect of cross diffusion in a competition model with stage structure, under homogeneous Neumann boundary condition. It will be shown that cross diffusion cannot only destabilize a uniform positive equilibrium, it can also help diffusion to induce instability of the uniform positive equilibrium. Moreover, stationary patterns can arise from the effect of cross diffusion.展开更多
The Three Gorges Reservoir is a good site for the further researches on reservoir induced seismicity due to decades＇ seismic monitoring. After the first water impounding in 2003, seismic activity becomes more frequen...The Three Gorges Reservoir is a good site for the further researches on reservoir induced seismicity due to decades＇ seismic monitoring. After the first water impounding in 2003, seismic activity becomes more frequent than that before water impoundment. In order to quantitatively study, the relationship between the water level fluctuation and earthquakes in TGR, we introduced statistical methods to attain the goal. First of all, we relocated the earthquakes in TGR region with double difference method and divided the earthquakes into 5 clusters with clustering analysis method. Secondly, to examine the impacts of water level fluctuation in different water filling stages on the seismic activity in the 5 clusters, a series of statistical analyses are applied. Pearson correlation results show that only the 175 m water level fluc- tuation has significantly positive impacts on the seismic activity in clusters I, II, III and V with correlation coefficients of 0.44, 0.38, 0.66 and 0.63. Cross-correlation analysis demonstrates that 0, ], 0 and 0 month time delay separately for the clusters I, II, III and V exists. It illustrated the influences of the water loading and pore pressure diffusion on induced earthquakes. Cointegration tests and impulse response analysis denoted that the 175 m water level only had long term and significant effects just on the seismic events in the intersection region of the Fairy Mount Fault and Nine-brook Fault. One standard deviation shock to 175 m water level increased the seismic activity in cluster V for the first 3 months, and then the negative influence was shown. After 7 months, the negative impulse response becomes stable. The long-term effect of the 175 m water impoundment also proved the important role of pore pressure diffusion in RIS with time.展开更多
We investigate the question whether certain parabolic systems in the sense of Petrovskii fulfill the resolvent estimate required for the generation of an analytic semigroup and apply the result to a problem concerning...We investigate the question whether certain parabolic systems in the sense of Petrovskii fulfill the resolvent estimate required for the generation of an analytic semigroup and apply the result to a problem concerning the diffusion of gases.展开更多
基金the National Natural Science Foundation of China (No.10401019)the DFG priority research program ANurnE (DFG Wa 633/9-2)National Natural Science Foundation of China (No. 10431060).
文摘This paper considers a kind of strongly coupled cross diffusion parabolic system, which can be used as the multi-dimensional Lyurnkis energy transport model in semiconductor science. The global existence and large time behavior are obtained for smooth solution to the initial boundary value problem. When the initial data are a small perturbation of an isothermal stationary solution, the smooth solution of the problem under the insulating boundary condition, converges to that stationary solution exponentially fast as time goes to infinity.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11272277,11572278,and 11572084)the Innovation Scientists and Technicians Troop Construction Projects of Henan Province,China(Grant No.2017JR0013)
文摘Cross-diffusion is a ubiquitous phenomenon in complex networks, but it is often neglected in the study of reaction–diffusion networks. In fact, network connections are often random. In this paper, we investigate pattern dynamics of random networks with cross-diffusion by using the method of network analysis and obtain a condition under which the network loses stability and Turing bifurcation occurs. In addition, we also derive the amplitude equation for the network and prove the stability of the amplitude equation which is also an effective tool to investigate pattern dynamics of the random network with cross diffusion. In the meantime, the pattern formation consistently matches the stability of the system and the amplitude equation is verified by simulations. A novel approach to the investigation of specific real systems was presented in this paper. Finally, the example and simulation used in this paper validate our theoretical results.
文摘The purpose of this paper is to study the effect of cross diffusion in a competition model with stage structure, under homogeneous Neumann boundary condition. It will be shown that cross diffusion cannot only destabilize a uniform positive equilibrium, it can also help diffusion to induce instability of the uniform positive equilibrium. Moreover, stationary patterns can arise from the effect of cross diffusion.
基金financially supported by the fund of the institute of seismology,China Earthquake Administration(IS201616254)National Natural Science Foundation of China(41572354,41304046)
文摘The Three Gorges Reservoir is a good site for the further researches on reservoir induced seismicity due to decades＇ seismic monitoring. After the first water impounding in 2003, seismic activity becomes more frequent than that before water impoundment. In order to quantitatively study, the relationship between the water level fluctuation and earthquakes in TGR, we introduced statistical methods to attain the goal. First of all, we relocated the earthquakes in TGR region with double difference method and divided the earthquakes into 5 clusters with clustering analysis method. Secondly, to examine the impacts of water level fluctuation in different water filling stages on the seismic activity in the 5 clusters, a series of statistical analyses are applied. Pearson correlation results show that only the 175 m water level fluc- tuation has significantly positive impacts on the seismic activity in clusters I, II, III and V with correlation coefficients of 0.44, 0.38, 0.66 and 0.63. Cross-correlation analysis demonstrates that 0, ], 0 and 0 month time delay separately for the clusters I, II, III and V exists. It illustrated the influences of the water loading and pore pressure diffusion on induced earthquakes. Cointegration tests and impulse response analysis denoted that the 175 m water level only had long term and significant effects just on the seismic events in the intersection region of the Fairy Mount Fault and Nine-brook Fault. One standard deviation shock to 175 m water level increased the seismic activity in cluster V for the first 3 months, and then the negative influence was shown. After 7 months, the negative impulse response becomes stable. The long-term effect of the 175 m water impoundment also proved the important role of pore pressure diffusion in RIS with time.
文摘We investigate the question whether certain parabolic systems in the sense of Petrovskii fulfill the resolvent estimate required for the generation of an analytic semigroup and apply the result to a problem concerning the diffusion of gases.
