This paper considers the following Cauchy problem for semilinear wave equations in n space dimensionswhere A is the wave operator, F is quadratic in (?) with (?) = ( ).The minimal value of s is determined such that th...This paper considers the following Cauchy problem for semilinear wave equations in n space dimensionswhere A is the wave operator, F is quadratic in (?) with (?) = ( ).The minimal value of s is determined such that the above Cauchy problem is locally well-posed in H8. It turns out that for the general equation s must satisfyThis is due to Ponce and Sideris (when n = 3) and Tataru (when n≥5). The purpose of this paper is to supplement with a proof in the case n = 2,4.展开更多
For ill-posed bilevel programming problem,the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model's satisfacto...For ill-posed bilevel programming problem,the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model's satisfactory degree in application.To acquire a more satisfying solution than the optimistic one to realize the two levels' most profits,this paper considers both levels' satisfactory degree and constructs a minimization problem of the two objective functions by weighted summation.Then,using the duality gap of the lower level as the penalty function,the authors transfer these two levels problem to a single one and propose a corresponding algorithm.Finally,the authors give an example to show a more satisfying solution than the optimistic solution can be achieved by this algorithm.展开更多
We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured b...We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured by a fractional differential operator, which is defined in the Riemann-Liouville sense, and a nonlinear term in which different solution components are coupled. The analysis is based on the reduction of the given system to an equivalent system of integral equations. By means of the nonlinear alternative of Leray-Schauder,the existence of solutions of the factional differential system is obtained. The uniqueness is established by using the Banach contraction principle.展开更多
In this paper, we prove the global existence and uniqueness of non-negative classical solutions of the Smoluchowski equation with viscosity ε>0. The existence of weak solutions when ε=0 is also obtained.
基金Project supported by the 973 Project of the National Natural Science Foundation of China,the Key Teachers Program and the Doctoral Program Foundation ofthe Miistry of Education of China.
文摘This paper considers the following Cauchy problem for semilinear wave equations in n space dimensionswhere A is the wave operator, F is quadratic in (?) with (?) = ( ).The minimal value of s is determined such that the above Cauchy problem is locally well-posed in H8. It turns out that for the general equation s must satisfyThis is due to Ponce and Sideris (when n = 3) and Tataru (when n≥5). The purpose of this paper is to supplement with a proof in the case n = 2,4.
基金supported by the National Science Foundation of China under Grant No.71171150the National Natural Science Foundation of ChinaTian Yuan Foundation under Grant No.11226226
文摘For ill-posed bilevel programming problem,the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model's satisfactory degree in application.To acquire a more satisfying solution than the optimistic one to realize the two levels' most profits,this paper considers both levels' satisfactory degree and constructs a minimization problem of the two objective functions by weighted summation.Then,using the duality gap of the lower level as the penalty function,the authors transfer these two levels problem to a single one and propose a corresponding algorithm.Finally,the authors give an example to show a more satisfying solution than the optimistic solution can be achieved by this algorithm.
基金supported by National Natural Science Foundation of China(Grant Nos.11471274,11421110001 and 91130002)Natural Science Foundation of Guizhou Province(Grant No.LKS[2013]04)
文摘We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured by a fractional differential operator, which is defined in the Riemann-Liouville sense, and a nonlinear term in which different solution components are coupled. The analysis is based on the reduction of the given system to an equivalent system of integral equations. By means of the nonlinear alternative of Leray-Schauder,the existence of solutions of the factional differential system is obtained. The uniqueness is established by using the Banach contraction principle.
基金This research is supported by the National Natural Science Foundation of China
文摘In this paper, we prove the global existence and uniqueness of non-negative classical solutions of the Smoluchowski equation with viscosity ε>0. The existence of weak solutions when ε=0 is also obtained.
