共查询到20条相似文献,搜索用时 156 毫秒
1.
Theorem1 Letm∈Nandm1,P(x)beanarbitraryorderpartialdifferentialopera-tor.Thenf(x,t),φj(x)∈J.(WhereJstandforthesetofanalyticfunctioninthispaper)t+P(x)mu=f(x,t)jutjt=0=φj(x) x∈Rn,t∈R1j=0,1,2,…,m-1.u(x,t)=∫t0(t-τ)m-1(m-1)!e-(t-τ)P(x)f(x,τ)dτ+e-… 相似文献
2.
3.
复数域上线性系统x=A(t)x,当A(t)=(aij(t))n×n具有(n,N,r) 差异性质且rn时,解的特征数j有估计λj-limt→∞1t∫tt0Reaj(τ)dτn-1r+1-nlimt→∞1t∫tt0A(τ)dτ,j=1,2,…,n,其中A(t)=max{|aij(t)|:i,j=1,2,…,n,i≠j.} 相似文献
4.
研 究如下第一边值 问题u t = div(| Du m |p - 2 Dum ) + f (x ,u)u (x ,t) = 0u (x ,0) = u0 0 (x ,t) ∈ Q T = Ω× (0, T)(x ,t) ∈ Ω× (0, T)x ∈ Ω解的极限性质 (t → ∞),推 广了文献[1 ~ 7] 的结果 相似文献
5.
§1. IntroductionInthispaper,westudytheexistenceandnonexistenceofglobalpositivesolutionsofthefollowingquasilinearparabolicequationswithnon-linearboundaryconditions:ut=1m△um-un, x∈Ω,t>01m·umγ=up,x∈Ω,t>0(1)u(x,0)=u0(x)>0,x∈Ω-wheren,m,parepositiveco… 相似文献
6.
§1. IntroductionWeconsiderthefollowingoptimizationproblem:(P) minx∈Xf(x)(1)whereX={x|x∈En,gj(x)≤0,j=1,2,…,m;gj(x)=0,j=m+1,…,m+l},letI={1,2,…,m},L={m+1,…,m+l}.Fortheproblem(P)withL=,manyefficientprojectiontypealgorithms[1-11]havebeenproposed.In[12],… 相似文献
7.
本文建立多线性算子TA1,A2,…Akf(x)=p.v∫RneiP(x,y)Ω(x-y)|x-y|n+M-kkj=1Rmj(Aj;x,y)f(y)dy,n2,的一个变形的sharp估计,其中P(x,y)是Rn×Rn上的实值多项式,Ω是零阶齐性函数且满足某种消失性条件,M=∑kj=1mj,Rmj(Aj;x,y)表示Aj在x点关于y的mj阶Taylor级数余项,对所有满足|α|=mj-1(j=1,2,…,k)的指标α,DαAj∈BMO(Rn).作为sharp估计的推论,得到了算子TA1,A2…Ak在Lp(1<p<∞)上的有界性. 相似文献
8.
设(Xi,Yi)1≤i≤n为来自二元总体(X,Y)的平稳,φ-混合样本,记m(x)△E(Y│X=x),m(x)的一种递推型核估计为mn(x)=n∑i=1hi^-1Yik((x-Xi)/hi)/n∑j=1h^-1jk(x-Xj)/hj)。本文在一定的条件下证明了(n/(n∑j=1h^-1j)^1/2)(mn(x1)-m(x1),mn(x2)-m(x2),...mn(xr0)-m(xr0))′依分布收 相似文献
9.
区间上平顶单峰扩张自映射的周期轨道 总被引:2,自引:0,他引:2
设t(0<t<1)是一个常数,n≥3是奇数,m≥0及k≥1是整数,P0(x)=x-1,Pi(x)=(x2i-1-1)Pi-1(x)(i≥1),rmn(t)及rk(t)分别是方程Pm(x)(x2mn-2x2m(n-2)-1)-t(x2mn-1)(x2m+1)=0及Pk-1(x)-t(x2k-1+1)=0在(1,+∞)上的唯一实根,f是闭区间I=[0,1]上的峰顶区间长度为t的平顶单峰扩张自映射.本文证明了,若f的扩张常数λ≥rmn(t)(或>rk(t)),,则f有2mn(或2k)周期点.此外,本文还指出,当1<λ<rmn(t)(或≤rk(t)时,在I上存在着具有扩张常数λ及峰顶区间长度t却无2mn(或2k)周期点的平顶单峰扩张自映射 相似文献
10.
带非线性边界条件的非线性抛物型方程组 总被引:1,自引:0,他引:1
本文讨论带非线性边界条件的抛物型方程组ut=Δum,vt=Δvm,x∈Ω,t>0,un=vp,vn=uq,x∈Ω,t>0,u(x,0)=u0(x)δ>0,v(x,0)=v0(x)δ>0,x∈Ω(I)解的整体存在性和在有限时刻爆破问题.其中m,p,q>0,ΩIRN是有界光滑区域,δ>0可以充分小. 相似文献
11.
The authors study the singular diffusion equationwhere Ω(?)Rn is a bounded domain with appropriately smooth boundary δΩ, ρ(x) = dist(x,δΩ), and prove that if α≥p-1, the equation admits a unique solution subject only to a given initial datum without any boundary value condition, while if 0 <α< p - 1, for a given initial datum, the equation admits different solutions for different boundary value conditions. 相似文献
12.
该文讨论Navier边值条件下的双调和特征值问题 Δ2u=λa(x)u+f(x, u), x∈ Ω, u=Δu=0, x∈ Ω,
解的存在性, 其中Ω RN(N ≥ 5)是有界光滑区域, Δ2为双调和算子, 权函数a(x)> 0 a. e. 于Ω, 且 a(x)∈Lr(Ω) (r ≥ N/4). 应用变分方法, 得出了在f(x, u)=0的情况下方程的第二特征值, 并研究了它的结构. 同时在f(x, u) 满足一定的条件下, 得出了共振与非共振情形下方程非零解的存在性 . 相似文献
13.
Chang C. Y. Dorea 《Probability Theory and Related Fields》1976,36(1):13-26
It is well known that for a large class of Markov process the associated semi-group T(t)f(x)=f(y)P(t,x;dy) satisfies the Kolmogorov backward differential equation, that is, if u(t,x)=T(t)f(x) then
and
.In this paper we are considering the opposite problem: given the diffusion and drift coefficients we study the differentiability preserving properties of the semigroup T(t) having as infinitesimal generator
.More specifically, for a large class of functions a(x) and b(x), we will prove for k=0, ..., 3 the existence of T(t) such that T(t): C
k
(I) C
k
(I) and the existence of a constant
k
such that |T(t)f|
k
|f|
k
exp (
k
t) for fC
k
(I). Moreover an explicit expression of
k
in terms of the coefficients a(x) and b(x) is obtained. As a side result we obtain the necessity of the boundary conditions imposed.This paper is a revised version of the author's Ph. D. dissertation at University of Massachusetts under W. Rosenkrantz 相似文献
14.
Mingxin Wang 《偏微分方程(英文版)》1995,8(3):273-280
This paper deals with the following semilinear parabolic equations with nonlinear boundary conditions u_t - Δu = f(u) - λu,x ∈ Ω, t > 0 \frac{∂u}{∂n} = g(u), \qquad x ∈ ∂Ω, t > 0 It is proved that every positive equilibrium solution is a threshold. 相似文献
15.
一类中立型时滞抛物偏微分方程的强迫振动性 总被引:14,自引:2,他引:12
罗李平 《数学的实践与认识》2005,35(10):182-189
研究了一类中立型时滞抛物偏微分方程:t(u(x,t)-pu(x,t-τ))-∑rk=1ak(t)Δu(x,t-ρk(t))+∑mj=1qj(t)u(x,t-σj(t))=e(x,t),的强迫振动性(其中(x,t)∈Ω×[0,∞)≡G,Ω是n维欧几里得空间Rn中带有逐段光滑边界Ω的有界区域,Δ是Rn中带有三类不同边值条件的拉普拉斯算子,强迫项e(x,t)是定义在G上的一个振荡函数),给出了一些新的振动性判据,这些结果推广了已知的一些结论. 相似文献
16.
Qin Tiehu 《数学年刊B辑(英文版)》1988,9(3):251-269
The paper deals with the following boundary problem of the second order quasilinear hyperbolic equation with a dissipative boundary condition on a part of the boundary:u_(tt)-sum from i,j=1 to n a_(ij)(Du)u_(x_ix_j)=0, in (0, ∞)×Ω,u|Γ_0=0,sum from i,j=1 to n, a_(ij)(Du)n_ju_x_i+b(Du)u_t|Γ_1=0,u|t=0=φ(x), u_t|t=0=ψ(x), in Ω, where Ω=Γ_0∪Γ_1, b(Du)≥b_0>0. Under some assumptions on the equation and domain, the author proves that there exists a global smooth solution for above problem with small data. 相似文献
17.
Wang Zhicheng 《数学年刊B辑(英文版)》1991,12(3):243-254
Consider the higher-order neutral delay differential equationd~t/dt~n(x(t)+sum from i=1 to lp_ix(t-τ_i)-sum from j=1 to mr_jx(t-ρ_j))+sum from k=1 to Nq_kx(t-u_k)=0,(A)where the coefficients and the delays are nonnegative constants with n≥2 even. Then anecessary and sufficient condition for the oscillation of (A) is that the characteristicequationλ~n+λ~nsum from i=1 to lp_ie~(-λτ_i-λ~n)sum from j=1 to mr_je~(-λρ_j)+sum from k=1 to Nq_ke~(-λρ_k)=0has no real roots. 相似文献
18.
Some Coneral Results on the First Boundry Value Problem for
Quasiliear Degenerate Parabolic Equation
In this paper, the authors investigate the first boundary value problem for equations of the form
$\[Lu = \frac{{\partial u}}{{\partial t}} - \frac{\partial }{{\partial {x_i}}}({a^{ij}}(u,x,t)\frac{{\partial u}}{{\partial {x_j}}}) - \frac{{\partial {f^i}(u,x,t)}}{{\partial {x_i}}} = g(u,x,t)\]$
with $a^ij(u,x,t)\xi_i\xi_j\geq 0$
An existence theorem of solution in BV_1,1/2(Q_T) is proved. The principal condition is that there exists \delta>0 such that for any (x, t)\in Q_T,|u|\geq M
$a^ij(u,x,t)\xi_i\xi_j-\delta\sum\limits_i,j=1^m(a_x^ij(u,x,t)\xi_i)^2\geq 0$ 相似文献
19.
The boundary behavior of the Bergman kernel function of a kind of Reinhardt domain is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points (Z,(Z-)). Let Ω be the Reinhardt domainm(X) where αj>0,j=1,2,…,n,N=N1+N2+…+Nn,‖Zj‖ is the standard Euclidean norm in CNj,j=1,2,…,n; and let K(Z,(W-)) be the Bergman kernel function of Ω. Then there exist two positive constants m and M,and a function F such that mF(Z,(Z-))≤K(Z,(Z-))≤MF(Z,(Z-))holds for every Z∈Ω. Here (X) and r(Z)=‖Z‖α-1 is the defining function of Ω. The constants m and M depend only on α=(α1,…,αn) and N1,N2,…,Nn,not on Z. This result extends some previous known results. 相似文献
20.
The C-regularity up to the boundary of solutions to the Dirichlet problem:
is proved, using a comparison principle of L with a Hörmander's type operator X
j
*
Xj, where is a smooth bounded open subset of Rn, and
is a second-order degenerate elliptic operator with smooth coefficients, satisfying the so-called Fefferman-Phong's condition. 相似文献