In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Und...In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Under some positivity condican be no global solutions no matter how展开更多
In this paper, the existence and nonexistence of finite travelling waves （FTWs） for a semilinear degenerate reaction-diffusion system (u<sub>i</sub><sup>αi</sup>t=u<sub>ixx</sub>...In this paper, the existence and nonexistence of finite travelling waves （FTWs） for a semilinear degenerate reaction-diffusion system (u<sub>i</sub><sup>αi</sup>t=u<sub>ixx</sub>-multiply from j=1 to N u<sub>j</sub><sup>mij</sup>, x∈R, t】0,i=1,. . . ,N （Ⅰ） is studied. where 0【a<sub>i</sub>【1. mij≥0 and sum from j=1 to N mij】0, i, j=1, . . . ,N .Necessary and sufficient conditions on existence and large time behaviours of FTWs of （Ⅰ） are obtained by using the matrix theory. Schauder’s fixed point theorem, and upper and lower solutious method.展开更多
The existence and uniqueness of the global smooth solution to the initial-boundary valueproblem of a system of multi-dimensions SRWE are proved. The sufficient conditions of 'blowingup' of the solution are given.
This paper considers the existence and asymptotic estimates of global solutions and finite time blowup of local solution of non-Newton filtration equation with special medium void of the following form:where , ft is a...This paper considers the existence and asymptotic estimates of global solutions and finite time blowup of local solution of non-Newton filtration equation with special medium void of the following form:where , ft is a smooth bounded domain in RN(N≥3), 0∈Ω, The result of asymptotic estimate of global solution depends on the best constant in Hardy inequality.展开更多
Particulate matter(PM)pollution has become a serious problem worldwide and various kinds of nanofibrous filters aiming to solve the problem have been developed.It is urgent to remove PM from high-temperature pollution...Particulate matter(PM)pollution has become a serious problem worldwide and various kinds of nanofibrous filters aiming to solve the problem have been developed.It is urgent to remove PM from high-temperature pollution sources,such as industrial emissions,coal furnaces,and automobile exhaust gases.However,filtration at pollution sources remains challenging because most existing air filters are not resistant to high temperature.Herein,heat-resistant polyimide(PI)nanofibrous air filters are fabricated via a simple and scalable solution blow-spinning method.These air filters show excellent thermal stability at high temperature up to 420℃.They exhibit a filtration efficiency as high as 99.73%at ambient temperature and over 97%at 300℃.In addition,a field test shows that the filters remove>97%of PM from the car exhaust fumes.Hence,the blow-spun PI nanofibrous membranes combined with the facile preparation strategy have great potential in high temperature air filtration fields and other similar applications such as water purification and protein separation.展开更多
This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichl...This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under appropriate hypotheses, the global existence and blow up in finite time of positive solutions are obtained. It is also proved that the blow up set is almost the whole domain. This differs from the local case. Furthermore, the blow up rate is precisely determined for the special case: f(u)=u p,p>1.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10225102)the 973 Project of the Ministry of Science and Technology of China.
文摘In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Under some positivity condican be no global solutions no matter how
基金Project supported by the Postdoctoral Science Foundation of China the Henan Province Natural Science Foundation of China
文摘In this paper, the existence and nonexistence of finite travelling waves （FTWs） for a semilinear degenerate reaction-diffusion system (u<sub>i</sub><sup>αi</sup>t=u<sub>ixx</sub>-multiply from j=1 to N u<sub>j</sub><sup>mij</sup>, x∈R, t】0,i=1,. . . ,N （Ⅰ） is studied. where 0【a<sub>i</sub>【1. mij≥0 and sum from j=1 to N mij】0, i, j=1, . . . ,N .Necessary and sufficient conditions on existence and large time behaviours of FTWs of （Ⅰ） are obtained by using the matrix theory. Schauder’s fixed point theorem, and upper and lower solutious method.
文摘The existence and uniqueness of the global smooth solution to the initial-boundary valueproblem of a system of multi-dimensions SRWE are proved. The sufficient conditions of 'blowingup' of the solution are given.
基金Supported by NSF of China(10171083),NSF of Fujian
文摘This paper considers the existence and asymptotic estimates of global solutions and finite time blowup of local solution of non-Newton filtration equation with special medium void of the following form:where , ft is a smooth bounded domain in RN(N≥3), 0∈Ω, The result of asymptotic estimate of global solution depends on the best constant in Hardy inequality.
基金This study was supported by the National Natural Science Foundation of China(Nos.51788104 and 51661135025)the National Basic Research Program of China(No.2015CB932500)China Postdoctoral Science Foundation(Nos.2018M640124 and 2019T120083).
文摘Particulate matter(PM)pollution has become a serious problem worldwide and various kinds of nanofibrous filters aiming to solve the problem have been developed.It is urgent to remove PM from high-temperature pollution sources,such as industrial emissions,coal furnaces,and automobile exhaust gases.However,filtration at pollution sources remains challenging because most existing air filters are not resistant to high temperature.Herein,heat-resistant polyimide(PI)nanofibrous air filters are fabricated via a simple and scalable solution blow-spinning method.These air filters show excellent thermal stability at high temperature up to 420℃.They exhibit a filtration efficiency as high as 99.73%at ambient temperature and over 97%at 300℃.In addition,a field test shows that the filters remove>97%of PM from the car exhaust fumes.Hence,the blow-spun PI nanofibrous membranes combined with the facile preparation strategy have great potential in high temperature air filtration fields and other similar applications such as water purification and protein separation.
文摘This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under appropriate hypotheses, the global existence and blow up in finite time of positive solutions are obtained. It is also proved that the blow up set is almost the whole domain. This differs from the local case. Furthermore, the blow up rate is precisely determined for the special case: f(u)=u p,p>1.
