查看更多>>摘要：We investigate the Cauchy problem for the sixth order p-generalized Benney-Luke equation.The local well-posedness is established in the energy space H1(Rn)∩H3(Rn)for 1 ≤ n ≤ 10,by means of the Sobolev multiplication law and the contrac-tion mapping principle.Moreover,we establish the energy identity of solutions and provide the sufficient conditions of the global existence of solutions by analyzing the properties of the energy functional.
查看更多>>摘要：It is well known that weak n-tilting modules are vital in tilting theory,which are generalizations of n-tilting and n-cotilting modules.The aim of this paper is to give a new characterization of weak n-tilting modules.In order to do that,we introduce the notion of weak n-star modules.We study more deeply the properties of them.Moreover,connections between(co)star and weak n-star modules are given.
查看更多>>摘要：In this paper,we consider the boundedness and compactness of the multi-linear singular integral operator on Morrey spaces,which is defined by TAf(x)=p.v.∫RnΩ(x-y)/|x-y|n+1R(A;x,y)f(y)dy,where R(A;x,y)=A(x)-A(y)-(V)A(y)·(x-y)with DβA∈BMO(Rn)for all|β|=1.We prove that TA is bounded and compact on Morrey spaces Lp,λ(Rn)for all 1＜p＜∞ withΩ and A satisfying some conditions.Moreover,the boundedness and compactness of the maximal multilinear singular integral operator TA,* on Morrey spaces are also given in this paper.
查看更多>>摘要：As a generalization of global mappings,we study a class of non-global map-pings in this note.Let A ⊆ B(H)be a von Neumann algebra without abelian direct summands.We prove that if a map δ:A →A satisfies δ([[A,B]*,C])=[[δ(A),B]*,C]+[[A,δ(B)]*,C]+[[A,B]*,δ(C)]for any A,B,C ∈ A with A*B*C=0,then δ is an additive*-derivation.As applications,our results are applied to factor von Neumann algebras,standard operator algebras,prime*-algebras and so on.
查看更多>>摘要：This paper is concerned with blow-up dynamics of solutions to coupled sys-tems of damped inhomogeneous wave equations with power nonlinearities related to weight function tα|x|β and variable boundary conditions on an exterior domain.The damping terms investigated in this work contain weak damping terms and convection terms.In terms of the Neumann-type boundary conditions and Dirichlet-type bound-ary conditions,the non-existence of global solutions to the problems is demonstrated by constructing appropriate test functions and applying contradiction arguments,re-spectively.Our main new contributions are that the effects of damping terms and non-linear terms on behaviors of solutions to the coupled inhomogeneous wave equations are analyzed.As far as the authors know,the results in Theorems 1.1-1.4 are new.
查看更多>>摘要：The initial boundary value problem for a compressible Euler system out-side a ball in R3 is considered in this paper.Assuming the initial data have small and compact supported perturbations near a constant state,we show that the solution will blow up in a finite time,and the lifespan estimate can be estimated by the small pa-rameter of the initial perturbations.To this end,a"tricky"test function admitting good behavior is introduced.
查看更多>>摘要：We present a formula for the third derivative of the distribution function of a regular function on a domain of Rn+1,and a further discussion of the extra assumption that the function is harmonic.The present work builds on[3,5].
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