共查询到20条相似文献,搜索用时 171 毫秒
1.
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
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该文研究了线性微分方程L(f)=f(k)+Ak-1(z)f(k-1)+ … +A0(z)f=F(z) (k∈ N)的复振荡理论, 其中系数Aj(z) (j=0, … , k-1)和F(z)是单位圆△={z:|z|<1}内的解析函数. 作者得到了几个关于微分方程解的超级, 零点的超收敛指数以及不动点的精确估计的定理. 相似文献
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刘梦云 《数学年刊A辑(中文版)》2022,43(3):251-262
本文研究了渐近欧氏流形上带有阻尼和位势的半线性波动方程的有限时间破裂以及解的生命跨度上界估计,其半线性项是形如c1 |ut|p + c2 |u|p的混合项. 该问题与Strauss猜测和Glassey猜测紧密相关. 相似文献
5.
彭志刚 《数学物理学报(A辑)》2008,28(5):945-957
设 H 是一个Hilbert空间. B(H) 表示所有H 到 H 的有界线性算子构成的Banach空间. 设 T= {f(z): f(z)=zI-∑∞n=2 znAn 在单位圆盘|z|<1上解析, 其中系数An是 H 到 H 的紧正Hermitian算子, I 表示 H 上的恒等算子, ∑∞n=2 n(An x, x) ≤1 对所有x ∈H, ∣|x∣∣=1 成立. 该文研究了函数族 T 的极值点. 相似文献
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对 0<α <∞, Nα 是开单位圆盘 D 上满足 sup z∈ D(1-|z|2)α f# (z)<∞ 的亚纯函数类, 其中 f# (z)=|f'(z)|/(1+|f(z)|2) 是 f 的球面导数. 该文给出了 D 上的 α -正规函数类的一些积分准则, 并用 Bergman-Carleson 测度的形式予以表示. 相似文献
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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
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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
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该文研究椭圆型方程
{Δpu+m|u|p-2u-Δqu+n|u|q-2u=g(x, u), x∈RN,
u∈ W1, p(RN)∩W1, q(RN)
弱解在全空间RN上的衰减性, 其中m, n ≥ 0, N≥3, 1 < q < p < N, g(x, u)关于u满足类渐近线性. 证明了该方程的
弱解在无穷远处关于|x|呈指数衰减性. 相似文献
11.
Mitsuhiro Nakao 《Mathematische Annalen》2001,320(1):11-31
We consider the initial-boundary value problem for the semilinear wave equation
where is an exterior domain in , is a dissipative term which is effective only near the 'critical part' of the boundary. We first give some estimates for the linear equation by combining the results of the local energy decay and estimates for the Cauchy problem in the whole space. Next, on the basis of these estimates we prove global existence of small
amplitude solutions for semilinear equations when is odd dimensional domain . When our result is applied if . We note that no geometrical condition on the boundary is imposed.
Received April 13, 2000 / Revised July 6, 2000 / Published online February 5, 2001 相似文献
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In this paper, we analyze the exponential decay property of solutions of the semilinear wave equation in with a damping term which is effective on the exterior of a ball. Under suitable and natural assumptions on the nonlinearity we prove that the exponential decay holds locally uniformly for finite energy solutions provided the nonlinearity is subcritical at infinity. Subcriticality means, roughly speaking, that the nonlinearity grows at infinity at most as a power p<5. The method of proof combines classical energy estimates for the linear wave equation allowing to estimate the total energy of solutions in terms of the energy localized in the exterior of a ball, Strichartz's estimates and results by P. Gérard on microlocal defect measures and linearizable sequences. We also give an application to the stabilization and controllability of the semilinear wave equation in a bounded domain under the same growth condition on the nonlinearity but provided the nonlinearity has been cut-off away from the boundary. 相似文献
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In this paper, we study the behavior of solutions of a semilinear elliptic equation in the exterior of a compact set as $|x| \to \infty $ . Such equations were considered by many authors (for example, Kondrat'ev, Landis, Oleinik, Veron, etc.). In the present paper, we study the case in which in the equation contains lower terms. The coefficients of the lower terms are arbitrary bounded measurable functions. It is shown that the solutions of the equation tend to zero as $|x| \to \infty $ . 相似文献
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This article proves the nonexistence of global solutions to a semilinear wave equation on an exterior domain in
\mathbbR2,{\mathbb{R}^2,} which is a part of Strauss’ conjecture. 相似文献
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This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. A Neumann condition is prescribed on the boundary of the holes.The presence of the holes does not allow to prove a compactness of the solutions in L2. To overcome this difficulty, the authors introduce a suitable auxiliary linear problem to which a corrector result is applied. Then, the asymptotic behaviour of the semilinear problem as ε→ 0 is described, and the limit equation is given. 相似文献
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The nonexistence of a global solution of the semilinear elliptic equation Δ2u ? (C/|x|4)u ? |x|σ|u|q = 0 in the exterior of a ball is studied. A sufficient condition for the nonexistence of a global solution is established. The proof is based on the test function method. 相似文献
17.
L. Chergui 《Journal of Evolution Equations》2009,9(2):405-418
For many evolution problems, a basic question is to establish convergence to equilibrium for globally defined solutions. This
type of result is well known for the semilinear wave equation with linear dissipation. In this paper, we are concerned with
the asymptotic behavior of global and bounded solutions of the following semilinear wave equation
with homogeneous Dirichlet boundary conditions and initial conditions. Here, α ≥ 0, is a bounded domain with sufficiently smooth boundary and is analytic in the second variable, uniformly with respect to the first one. In this paper, we suppose that the set of stationary
solutions is compact and we prove convergence of global and bounded solutions to an equilibrium, for some small value of α depending on the nonlinearity f. The case α = 0 corresponds to the wave equation with linear dissipation which is solved by Haraux and Jendoubi (Calc Var Partial Differ
Equ 9:95–124, 1999). 相似文献
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This paper is devoted to studying initial-boundary value problems for semilinear wave equations and derivative semilinear wave equations with variable coefficients on exterior domain with subcritical exponents in n space dimensions. We will establish blow-up results for the initial-boundary value problems. It is proved that there can be no global solutions no matter how small the initial data are, and also we give the life span estimate of solutions for the problems. 相似文献
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In this paper, the uniqueness of stationary solutions with vacuum of Euler-Poisson equations is considered. Through a nonlineax transformation which is a functionof density and entropy the corresponding problem can be reduced to a semilinear ellipticequation with a nonlinear source term consisting of a power function, for which the classical 相似文献
20.
Gabriel R. Barrenehea Mauricio A. Barrientos Gabriel N. Gatica 《Numerical Functional Analysis & Optimization》2013,34(7-8):705-735
We provide the numerical analysis of the combination of finite elements and Dirichlet-to-Neumann mappings (based on boundary integral operators) for a class of nonlinear exterior transmission problems whose weak formulations reduce to Lipschitz-continuous and strongly monotone operator equations. As a model we consider a nonlinear second order elliptic equation in divergence form in a bounded inner region of the plane, coupled with the Laplace equation in the corresponding unbounded exterior part. A discrete Galerkin scheme is presented by using linear finite elements on a triangulation of the domain, and then applying numerical quadrature and analytical formulae to evaluate all the linear, bilinear and semilinear forms involved. We prove the unique solvability of the discrete equations, and show the strong convergence of the approximate solutions. Furthermore, assuming additional regularity on the solution of the continuous operator equation, the asymptotic rate of convergence O(h) is also derived. Finally, numerical experiments are presented, which confirm the convergence results. 相似文献