The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonemp...The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonempty subset in a strictly convex Kadec Banach space. Further, we prove that the set of all points inE(G) such that the best simultaneous approximation problems are not well posed is a u- porous set inE(G) whenX is a uniformly convex Banach space. In addition, we also investigate the generic property of the ambiguous loci of the best simultaneous approximation.展开更多
The initial value problem for the generalized Korteweg-deVries equation of order three on the line is shown to be globally well posed for rough data. Our proof is based on the multilinear estimate and the I-method int...The initial value problem for the generalized Korteweg-deVries equation of order three on the line is shown to be globally well posed for rough data. Our proof is based on the multilinear estimate and the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao.展开更多
Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let denote the space of all non-empty compact convex subsets of X endowed with ...Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let denote the closure of the set . We prove that the set of all , such that the minimization (resp. maximization) problem min(A,G) (resp. max(A,G)) is well posed, contains a dense G δ-subset of , thus extending the recent results due to Blasi, Myjak and Papini and Li.展开更多
This paper studies first order semilinear hyperbolic systems in n(n≥2)space dimensions.Under the hypothesis that the system satisfies so called`null condition',the local well posedness for its Cauchy problem with...This paper studies first order semilinear hyperbolic systems in n(n≥2)space dimensions.Under the hypothesis that the system satisfies so called`null condition',the local well posedness for its Cauchy problem with initial data in H n-12 is proved.展开更多
基金the National Natural Science Foundation of China (Grant No. 19971013) and Natural Science Foundation of Jiangsu Province (Grant No. BK99001) .
文摘The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonempty subset in a strictly convex Kadec Banach space. Further, we prove that the set of all points inE(G) such that the best simultaneous approximation problems are not well posed is a u- porous set inE(G) whenX is a uniformly convex Banach space. In addition, we also investigate the generic property of the ambiguous loci of the best simultaneous approximation.
文摘The initial value problem for the generalized Korteweg-deVries equation of order three on the line is shown to be globally well posed for rough data. Our proof is based on the multilinear estimate and the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao.
基金partly supported by the National Natural Science Foundation of China(Grant No,10271025)
文摘Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let denote the closure of the set . We prove that the set of all , such that the minimization (resp. maximization) problem min(A,G) (resp. max(A,G)) is well posed, contains a dense G δ-subset of , thus extending the recent results due to Blasi, Myjak and Papini and Li.
文摘This paper studies first order semilinear hyperbolic systems in n(n≥2)space dimensions.Under the hypothesis that the system satisfies so called`null condition',the local well posedness for its Cauchy problem with initial data in H n-12 is proved.
