一类非线性抛物方程Cauchy问题解的存在性条件

研究了带源项的非线性抛物方程Cauchy问题解存在的必要条件以及解所应具有的性质,通过把文献中的线性算子推广到形式较一般的带源项的非线性抛物算子,利用其中处理线性问题的方法来处理非线性问题．     

一类退化抛物方程解的几何性质

本文讨论非线性退化抛物方程u_t=△φ(u)的Cauchy问题弱解u(x,t)的正则性与几何性质.本文证明:若正数β足够大,则曲面ψ=ψ(x,t)=[φ(u)]~β是随时间t的连续变化而漂浮于空间R~(n+1)中的n维完备黎曼流形,它与实欧氏空R~n相切于低维流形(?)H_n(t),而H_u(t)={x∈R~n:u(x,t)0);函数ψ(x,t)在经典的意义下满足另一退化抛物方程.     

一类积集上的广义向量变分不等式

研究一类积集上具某种权向量的广义向量变分不等式组及其广义向量变分不等式的有关问题,刻画它们之间解的相互关系.在映射的次连续性和关于某向量广义单调性的条件下,利用集值映射的不动点定理,对所讨论的几种类型的广义向量变分不等式给出解的存在性.     

A Conservative Difference Scheme for Conservative Differential Equation with Periodic Boundary

1　ＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎａｎｄＤｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙＰｒｏｐｅｒｔｉｅｓｏｆｔｈｅＳｏｌｕｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ,ｗｅｃｏｎｓｉｄｅｒｔｈｅｃｏｎｓｅｒｖａｔｉｖｅｆｏｒｍａｎｄｓｉｎｇｕｌａｒｐｅｒｔｕｒｂｅｄｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｗｉｔｈｐｅｒｉｏｄｉｃｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ :Ｌｕ(ｘ) ≡ε(ｐ(ｘ)ｕ′(ｘ) )′ (ｑ(ｘ)ｕ(ｘ) )′-ｒ(ｘ)ｕ(ｘ) =ｆ(ｘ)　　( 0 <ｘ<1 ) ,( 1 )ｕ( 0 ) ≡ｕ( 1 ) ,ｌｕ≡ｕ′( 1 )…     

Representation of measures of noncompactness and its applications related to an initial value problem in Banach spaces

Science China Mathematics - This paper is devoted to studying the representation of measures of non-generalized compactness, in particular, measures of noncompactness, of non-weak compactness and...     

Ramanujan-style proof of $$p_{-3}(11n+7) \equiv 0\ (\mathrm{mod\ }11)$$

In this note, we establish two identities of \((q;\,q)_\infty ^8\) by using Jacobi’s four-square theorem and two of Ramanujan’s identities. As an important consequence, we present one Ramanujan-style proof of the congruence \(p_{-3}(11n+7)\equiv 0\ (\mathrm{mod\ }11)\), where \(p_{-3}(n)\) denotes the number of 3-color partitions of n.