This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space.With the help of linear time-space estimates,we establish the local e...This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space.With the help of linear time-space estimates,we establish the local existence and uniqueness of solutions by means of the contraction mapping principle.The global existence and blow-up of the solutions at both subcritical and critical initial energy levels are obtained.Moreover,we construct the sufficient conditions of finite time blow-up of the solutions with arbitrary positive initial energy.展开更多
Featuring exceptional mechanical and functional performance, MWCNTs and graphene(nano)platelets(GNPs or Gn Ps;each platelet below 10 nm in thickness) have been increasingly used for the development of polymer nanocomp...Featuring exceptional mechanical and functional performance, MWCNTs and graphene(nano)platelets(GNPs or Gn Ps;each platelet below 10 nm in thickness) have been increasingly used for the development of polymer nanocomposites. Since MWCNTs are now cost-effective at US$30 per kg for industrial applications, this work starts by briefly reviewing the disentanglement and surface modification of MWCNTs as well as the properties of the resulting polymer nanocomposites. GNPs can be made through the thermal treatment of graphite intercalation compounds followed by ultrasonication;GNPs would have lower cost yet higher electrical conductivity over 1,400 S cmthan MWCNTs. Through proper surface modification and compounding techniques, both types of fillers can reinforce or toughen polymers and simultaneously add anti-static performance. A high ratio of MWCNTs to GNPs would increase the synergy for polymers. Green, solvent-free systhesis methods are desired for polymer nanocomposites. Perspectives on the limitations, current challenges and future prospects are provided.展开更多
基金supported by the National Natural Science Foundation of China(12301272)the Natural Science Foundation of Henan(202300410109)the Cultivation Programme for Young Backbone Teachers in Henan University of Technology,and the Innovative Funds Plan of Henan University of Technology(2020ZKCJ09).
文摘This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space.With the help of linear time-space estimates,we establish the local existence and uniqueness of solutions by means of the contraction mapping principle.The global existence and blow-up of the solutions at both subcritical and critical initial energy levels are obtained.Moreover,we construct the sufficient conditions of finite time blow-up of the solutions with arbitrary positive initial energy.
基金financial support by the Australian Research Council (LP180100005 & DP200101737)。
文摘Featuring exceptional mechanical and functional performance, MWCNTs and graphene(nano)platelets(GNPs or Gn Ps;each platelet below 10 nm in thickness) have been increasingly used for the development of polymer nanocomposites. Since MWCNTs are now cost-effective at US$30 per kg for industrial applications, this work starts by briefly reviewing the disentanglement and surface modification of MWCNTs as well as the properties of the resulting polymer nanocomposites. GNPs can be made through the thermal treatment of graphite intercalation compounds followed by ultrasonication;GNPs would have lower cost yet higher electrical conductivity over 1,400 S cmthan MWCNTs. Through proper surface modification and compounding techniques, both types of fillers can reinforce or toughen polymers and simultaneously add anti-static performance. A high ratio of MWCNTs to GNPs would increase the synergy for polymers. Green, solvent-free systhesis methods are desired for polymer nanocomposites. Perspectives on the limitations, current challenges and future prospects are provided.
