We study the blowing-up X of a smooth projective variety X along a smooth center B that is equipped with a projective bundle structure over a variety Z.If the Picard number p(X)is 1 and dim X is at most 4,we classify ...We study the blowing-up X of a smooth projective variety X along a smooth center B that is equipped with a projective bundle structure over a variety Z.If the Picard number p(X)is 1 and dim X is at most 4,we classify all such pairs(X,B).If X is a projective space P_(n)(n≥5)and dim B is 2,we show that B is a linear subspace in X.展开更多
In this paper, we show that all the nontrivial valuations on surfaces can be given by the infinite sequences of blowing-ups, and give the process of blowing-ups.
This paper gives the existence of a duck solution in a slow-fast system in R2+2 using two ways. One is an indirect way and the other is a direct way. In the indirect way, the original system is once reduced to the slo...This paper gives the existence of a duck solution in a slow-fast system in R2+2 using two ways. One is an indirect way and the other is a direct way. In the indirect way, the original system is once reduced to the slow-fast system in R2+1. In the direct one, it has a 4-dimensional duck solution when having an efficient local model. This is already published in [1,2]. Some sufficient conditions are given to get such a good model.展开更多
This paper concerns the asymptotic behavior of solutions to one-dimensional semilinear parabolic equations with boundary degeneracy both in bounded and unbounded intervals.For the problem in a bounded inter-val,it is ...This paper concerns the asymptotic behavior of solutions to one-dimensional semilinear parabolic equations with boundary degeneracy both in bounded and unbounded intervals.For the problem in a bounded inter-val,it is shown that there exist both nontrivial global solutions for small initial data and blowing-up solutions for large one if the degeneracy is not strong.Whereas in the case that the degeneracy is strong enough,the nontrivial solu-tion must blow up in a finite time.For the problem in an unbounded interval,blowing-up theorems of Fujita type are established.It is shown that the critical Fujita exponent depends on the degeneracy of the equation and the asymptotic behavior of the diffusion coefficient at infinity,and it may be equal to one or infinity.Furthermore,the critical case is proved to belong to the blowing-up case.展开更多
基金supported by National Natural Science Foundation of China(12001547)Guangdong Basic and Applied Basic Research Foundation(2019A1515110907).
文摘We study the blowing-up X of a smooth projective variety X along a smooth center B that is equipped with a projective bundle structure over a variety Z.If the Picard number p(X)is 1 and dim X is at most 4,we classify all such pairs(X,B).If X is a projective space P_(n)(n≥5)and dim B is 2,we show that B is a linear subspace in X.
文摘In this paper, we show that all the nontrivial valuations on surfaces can be given by the infinite sequences of blowing-ups, and give the process of blowing-ups.
文摘This paper gives the existence of a duck solution in a slow-fast system in R2+2 using two ways. One is an indirect way and the other is a direct way. In the indirect way, the original system is once reduced to the slow-fast system in R2+1. In the direct one, it has a 4-dimensional duck solution when having an efficient local model. This is already published in [1,2]. Some sufficient conditions are given to get such a good model.
基金This work was supported by the National Key R&D Program of China(Grant No.2020YFA0714i01)by the National Natural Science Foundation of China(Grant No.11925105).
文摘This paper concerns the asymptotic behavior of solutions to one-dimensional semilinear parabolic equations with boundary degeneracy both in bounded and unbounded intervals.For the problem in a bounded inter-val,it is shown that there exist both nontrivial global solutions for small initial data and blowing-up solutions for large one if the degeneracy is not strong.Whereas in the case that the degeneracy is strong enough,the nontrivial solu-tion must blow up in a finite time.For the problem in an unbounded interval,blowing-up theorems of Fujita type are established.It is shown that the critical Fujita exponent depends on the degeneracy of the equation and the asymptotic behavior of the diffusion coefficient at infinity,and it may be equal to one or infinity.Furthermore,the critical case is proved to belong to the blowing-up case.
