共查询到20条相似文献,搜索用时 62 毫秒
1.
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
2.
矩阵微分方程经常出现在许多物理模型和工程技术模型中.利用矩阵样条构造形如{y(p)(x)=Ap-1(x)y(p-1)(x)+Ap-2(x)y(p-2)(x)+…+A1(x)y(1)(x)+A0(x)y(x)+B0(x),y(a)=ya,…,y(p-1)(a)=y(p-1)a,x∈[a,b];Ai(x),B0(x)∈C4[a,b],0≤i≤p-烅烄烆1的高阶矩阵线性微分方程初值问题的数值解.给出实现算法和数值解的近似误差估计以及数值实例.先将高阶矩阵微分方程转化为一阶矩阵微分方程,然后利用三次矩阵样条求出一阶矩阵线性微分方程的数值解,从而解决高阶微分方程问题. 相似文献
3.
栗付才 《数学物理学报(A辑)》2008,28(6):1187-1193
该文研究光滑有界区域Ω( RN (N≥ 1) 上具有齐次Dirichlet边界条件的拟线性退化抛物型方程组
ut-div(|▽u|p-2 ▽u) =avα, vt-div(|▽v|q-2 ▽v) =buβ
的非负解的性质, 其中p, q>2, α, β ≥ 1, a, b> 0是常数. 该文指出上述方程组的解是否在有限时刻爆破依赖于初值、系数 a 与 b以及 αβ 和 (p-1)(q-1)之间的关系. 相似文献
4.
<正> 本文是這系列著作中Ⅱ的一個補充.在Ⅱ中(參閱Ⅱ的更正)我們證明了可微分閉流形的某些示性類特別是法3示性類的拓撲不變性.它的證明是隱合的(implicit).本文目的在進一步求得這些示性類用流形同調構造來表示的顧谿(explicit)公式,使我們能就任意可定向的可微分閉流形的這些示性類進行具體的計算.特別可以獲得下述結果: 相似文献
5.
对f∈Lp(R+,Δ(t)dt),Δ(t)=(2sinht)2α+1(2cosht)2β+1,1p2,本文证明了当Rez>(2/p-1)(α+1/2)时,f的Fourier-Jacobi展开的z-阶Riesz平均几乎处处收敛于f.该结果推广了Giulini和Mauceri在实秩为1的对称空间上的相应结果 相似文献
6.
证明了若权函数(u,v)满足下列A_p型条件:对δ>0及任意的方体Q, |Q|~(pα/n)‖u‖L(log L)~(2p-1+δ),Q(1/|Q|∫_Qv(x))-(p′/pdx)~(p/p′)≤K<∞,则分数次积分算子I_α,0<α<n,是从L~p(v)到L~(p,∞)(u)的有界算子,1<p<∞. 相似文献
7.
该文利用变分方法讨论了方程 -△p u=λa(x)(u+)p-1-μa(x)(u-)p-1+f(x, u), u∈W01,p(\Omega)在(λ, μ)\not\in ∑p和(λ, μ) ∈ ∑p 两种情况下的可解性, 其中\Omega是 RN(N≥3)中的有界光滑区域, ∑p为方程 -△p u=α a(x)(u+)p-1-βa(x)(u-)p-1, u∈ W01,p(\Omega)的Fucik谱, 权重函数a(x)∈ Lr(\Omega) (r≥ N/p)$且a(x)>0 a.e.于\Omega, f满足一定的条件. 相似文献
8.
Huashui ZHAN 《数学年刊B辑(英文版)》2012,33(5):767-782
Consider the following Cauchy problem:u_t = div(|▽u ~m |~ p-2▽u~m),(x,t) ∈ST=R~N ×(0,T),u(x,0) = μ,x ∈R~N,where 1
相似文献
9.
A. Messaoudi Salim 《偏微分方程(英文版)》2001,14(2):105-110
We consider a semilinear wave equation of the form u_tt(x, t) - Δu(x, t) = - m(x, t)u_t(x, t) + ∇Φ(x) ⋅ ∇u(x, t ) + b(x)|u(x, t)|^{p-2}u(x, t) where p > 2. We show, under suitable conditions on m, Φ, b, that weak solutions break down in finite time if the initial energy is negative. This result improves an earlier one by the author [1]. 相似文献
10.
In this paper, we present a necessary and suffcient condition that the perturbed monomial mapping is ergodic on a sphere S_(p-1)(1), which is in a combination with Anashin's earlier results about the perturbed monomial ergodic mappings on a sphere S_(p-r)(1), r 1, completely solve a problem posed by A. Khrennikov about the ergodicity of a perturbed monomial mapping on a sphere. 相似文献
11.
12.
In this paper,the asymptotic behavior of a non-local hyperbolic problem modelling Ohmic heating is studied.It is found that the behavior of the solution of the hyperbolic problem only has three cases:the solution is globally bounded and the unique steady state is globally asymptotically stable;the solution is infinite when t→∞;the solution blows up.If the solution blows up,the blow-up is uniform on any compact subsets of(0,1] and the blow-up rate is lim t → T*-u(x,t)(T*-t)1/α+βp-1=(α+βp-1/1-α)1/1-α-βp,where T* is the blow-up time. 相似文献
13.
In this paper, the traveling wave solutions for a generalized Camassa-Holm equation $u_t-u_{xxt}=\frac{1}{2}(p+1)(p+2)u^pu_x-\frac{1}{2}p(p-1)u^{p-2}u_x^3-2pu^{p-1}u_xu_{xx}-u^pu_{xxx}$ are investigated. By using the bifurcation method of dynamical systems, three major results for this equation are highlighted. First, there are one or two singular straight lines in the two-dimensional system under some different conditions. Second, all the bifurcations of the generalized Camassa-Holm equation are given for $p$ either positive or negative integer. Third, we prove that
the corresponding traveling wave system of this equation possesses peakon, smooth solitary wave solution, kink and anti-kink wave solution, and periodic wave solutions. 相似文献
14.
讨论了一类非守恒相场模型解的性态,证明当a2p - 1 < 0 及初值充分大时解在有限时刻 blow up. 相似文献
15.
本文构造了在Adams谱序列中由hng0γ3∈E26,t所表示的球面稳定同伦群πt-6S的新元素族,回访了文[1]中构造的bn-1g0γ3-元素族∈πt-7S,其中t=2pn(p-1)+6(p2+P+1)(p-1),P≥7是素数, n≥4. 相似文献
16.
In this paper,we give a metheod to obtain genus of the torus knot by some regular projection of the torus knot and have proved that the penus of the torus knot of type p,q is(p-1)(q-1). 相似文献
17.
Verena Bögelein Mikko Parviainen 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(1):21-54
We establish global regularity results for a wide class of non-linear higher order parabolic systems. The model problem we have in mind is the parabolic p-Laplacian system of order 2m, m ≥ 1, $\partial_t u + (-1)^{m}\, {\rm div}^m \left(|D^mu|^{p-2}D^{m}u\right) = 0$ with prescribed boundary and initial values. We prove that if the boundary values are sufficiently regular, then D m u is globally integrable to a better power than the natural p. The method also produces a global estimate. 相似文献
18.
本文主要在Lp范数逼近意义下确定一类拟Hermite-Fejr插值多项式列在一重积分Wiener空间下平均误差的弱渐近阶.结果说明若概率空间不同,插值算子列在平均误差的意义下可能具有完全不同的逼近性质.在某些特殊情形下得到了其值或强渐近阶. 相似文献
19.
This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form (un)t = (|ux|m-1ux)x up in (0, 1) × (0, T) subject to nonlinear boundary source (|ux|m-1ux)(1,t) = uq(1,t), (|ux|m-1ux)(0,t) = 0, and positive initial data u(x,0) = uo(x), where the parameters m, n, p, q > 0.It is proved that the problem possesses global solutions if and only if p ≤ n and q≤min{n, m(n 1)/ m 1}. 相似文献
20.
本文讨论了Ω上如下一类带临界增长的椭圆方程在拟超临界的Neumann边界条件下正解的存在性:-Div(| u |p-2 u) =λum up*-1,-| u |p-2 u ν=ψ(x)uq-1,x∈Ω,x∈Ω.这里Ω∈RN,(N≥3)是光滑有界区域, 1≤p < N,0< m < p-1,(N -1)pN - p= p*N-1 ≤q < p*,其中p* =NpN - p是W1,p(Ω)→Ls(Ω)的Sobolev临界指数,p*N-1 =(N -1)pN - p是W1,p(Ω)→Lt( Ω)的在(N-1)维流形上的临界指数,λ>0是一个正参数. 相似文献