THE continental dynamics has become a goaI since the beginning of the 1990s and it will still bethe key subject in the 21st century. Orogenic belts, having experienced the most intensechanges of geotherm and mechanics...THE continental dynamics has become a goaI since the beginning of the 1990s and it will still bethe key subject in the 21st century. Orogenic belts, having experienced the most intensechanges of geotherm and mechanics in the lithosphere, are the important research object in thestudy of continental dynamics. For this reason, the study of orogenic belts forms a hot and dif-ficult point in the geological society and the concentration of efforts is needed for overcomingthis difficult point. China has the most orogenic belts of various types in the world, so the De-partment of Earth Sciences caught this scientific chance in the early 1990s, took the展开更多
IN recent years, a series of environmental problems have attracted wide attention in the world.As environmental changes can result from both the operations of natural factors and human ac-tivities, the international s...IN recent years, a series of environmental problems have attracted wide attention in the world.As environmental changes can result from both the operations of natural factors and human ac-tivities, the international science community has the common opinion that environmental prob-lems should be studied in a broader perspect. In other words, the earth environment should beregarded as an entity that consists of many interactive and interrelated parts. Highlighted展开更多
Any weak solution u to the Navier-Stokes equations is showed to be regular under the assumption that ||u|| L 2w (0,T ;L ∞ ( R 3 )) is sufficiently small, which is a limiting case of the regularity criteria derived by...Any weak solution u to the Navier-Stokes equations is showed to be regular under the assumption that ||u|| L 2w (0,T ;L ∞ ( R 3 )) is sufficiently small, which is a limiting case of the regularity criteria derived by Kim and Kozono. Our result gives a positive answer to the question proposed by Kim and Kozono. For the incompressible magnetohydrodynamic equations, we also show the regularity of weak solution only under the assumption that ||u|| L 2w (0,T ;L ∞ ( R 3 )) is sufficiently small.展开更多
It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) > 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a...It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) > 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:ut-△f(u) = 0,x ∈ Rn.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping:utt + utt+ △f(u) = 0,x ∈ Rn.The time decay rate is also obtained.The proofs are given by an elementary energy method.展开更多
文摘THE continental dynamics has become a goaI since the beginning of the 1990s and it will still bethe key subject in the 21st century. Orogenic belts, having experienced the most intensechanges of geotherm and mechanics in the lithosphere, are the important research object in thestudy of continental dynamics. For this reason, the study of orogenic belts forms a hot and dif-ficult point in the geological society and the concentration of efforts is needed for overcomingthis difficult point. China has the most orogenic belts of various types in the world, so the De-partment of Earth Sciences caught this scientific chance in the early 1990s, took the
文摘IN recent years, a series of environmental problems have attracted wide attention in the world.As environmental changes can result from both the operations of natural factors and human ac-tivities, the international science community has the common opinion that environmental prob-lems should be studied in a broader perspect. In other words, the earth environment should beregarded as an entity that consists of many interactive and interrelated parts. Highlighted
基金supported by the National Basic Research Program of China (973 Program) (Grant No. 2006CB805902)Knowledge Innovation Funds of Chinese Academy of Sciences (Grant No.KJCX3-SYW-S03)
文摘Any weak solution u to the Navier-Stokes equations is showed to be regular under the assumption that ||u|| L 2w (0,T ;L ∞ ( R 3 )) is sufficiently small, which is a limiting case of the regularity criteria derived by Kim and Kozono. Our result gives a positive answer to the question proposed by Kim and Kozono. For the incompressible magnetohydrodynamic equations, we also show the regularity of weak solution only under the assumption that ||u|| L 2w (0,T ;L ∞ ( R 3 )) is sufficiently small.
基金supported in part by National Basic Research Program of China (GrantNo. 2006CB805902)supported in part by National Natural Science Foundation of China for Distinguished Youth Scholar (Grant No. 10825102)+1 种基金NSFC-NSAF (Grant No. 10676037)National Basic Research Program of China (Grant No. 2006CB805902)
文摘It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) > 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:ut-△f(u) = 0,x ∈ Rn.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping:utt + utt+ △f(u) = 0,x ∈ Rn.The time decay rate is also obtained.The proofs are given by an elementary energy method.
