This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l ＋ u^p1v^q1 and vt = △v ^m ＋ u^p2 v^q2 with homogeneous Dirichlet boundary conditions....This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l ＋ u^p1v^q1 and vt = △v ^m ＋ u^p2 v^q2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1 - （l -p1）（m- q2）, the initial data, and the domain Ω.展开更多
In this paper we explicitly determine the derivation algebra of a quasi Rn-filiform Lie algebra and prove that a quasi Rn-filiform Lie algebra is a completable nilpotent Lie algebra.
In this paper, we study the Lie algebras in which every subspace is its subalgebra （denoted by HB Lie algebras）. We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g＋Cidg, ...In this paper, we study the Lie algebras in which every subspace is its subalgebra （denoted by HB Lie algebras）. We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g＋Cidg, where g is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.展开更多
We discuss a class of filiform Lie superalgebras Ln,m. From these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of Der0（Ln,m） and Dery（Ln,m）. B...We discuss a class of filiform Lie superalgebras Ln,m. From these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of Der0（Ln,m） and Dery（Ln,m）. By computing a maximal torus on each Ln,m, we show that Ln,m are completable nilpotent Lie superalgebras. We also view Ln,m as Lie algebras, prove that Ln,m are of maximal rank, and show that Ln,m are completable nilpotent Lie algebras. As an application of the results, we show a Heisenberg superalgebra is a completable nilpotent Lie superalgebra.展开更多
基金This work is supported in part by NNSF of China (10571126)in part by Program for New Century Excellent Talents in University.
文摘This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l ＋ u^p1v^q1 and vt = △v ^m ＋ u^p2 v^q2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1 - （l -p1）（m- q2）, the initial data, and the domain Ω.
文摘In this paper we explicitly determine the derivation algebra of a quasi Rn-filiform Lie algebra and prove that a quasi Rn-filiform Lie algebra is a completable nilpotent Lie algebra.
文摘In this paper, we study the Lie algebras in which every subspace is its subalgebra （denoted by HB Lie algebras）. We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g＋Cidg, where g is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.
文摘We discuss a class of filiform Lie superalgebras Ln,m. From these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of Der0（Ln,m） and Dery（Ln,m）. By computing a maximal torus on each Ln,m, we show that Ln,m are completable nilpotent Lie superalgebras. We also view Ln,m as Lie algebras, prove that Ln,m are of maximal rank, and show that Ln,m are completable nilpotent Lie algebras. As an application of the results, we show a Heisenberg superalgebra is a completable nilpotent Lie superalgebra.
