共查询到20条相似文献,搜索用时 203 毫秒
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该文运用Fokas方法分析了高阶Chen-Lee-Liu方程在半直线上的初边值问题,证明了高阶Chen-Lee-Liu方程初边值问题的解可以用复λ平面上的矩阵Riemann-Hilbert问题的形式解唯一表示. 相似文献
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混合元解重调和方程的条件数 总被引:2,自引:1,他引:1
考虑重调和方程第一边值问题Ω是R~2中的有界多边形区域。根据[1,381—424],问题可转化为 找(u,φ)∈H~1(Ω)×H_0~1(Ω),使成立 相似文献
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本文考虑使用修正的有理谱方法处理半直线上的BBM方程初边值问题.对非线性项使用Chebyshev有理插值显式处理,而线性项使用修正Legendre有理谱方法隐式处理.这种处理既可以节约运算又可以保持良好的稳定性.数值例子表明了算法的有效性 相似文献
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本文证明了无界区域上三维趋化模型初边值问题全局小强解的存在性.此外还研究了系统在半空间上的收敛性,证明了在H~1中,强解以(1+t)-3/4速率收敛到其相应的稳态解. 相似文献
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本文讨论如下抛物型Monge-Ampere方程的第一初边值问题-ut+det1/nD2u=g(x,t),(x,t)∈Q=Ω×(0,T],u=ψ(z,t),(z,t)∈apQ,其中Ω为Rn中有界凸集.证明了在更一般的结构条件下[3,7]的结果仍然成立.证明中重要的一点是在Rn×R中非柱型域上"冻结问题"的可解性. 相似文献
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本文研究具有惯性项和阻尼项的亚三次非线性Cahn-Hilliard方程的初边值问题.在非线性弱正则的条件下,我们建立弱解的适定性,而不考虑非线性项的一阶导数的下界条件.接着利用弱解的渐近紧和能量解的严格Lyapunov函数的存在性,证明在空间(H~2(?)∩H_0~1(?))×L~2(?)上存在整体吸引子. 相似文献
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我们证明了半空间中一维可压Navier—Stokes方程初边值问题局部解的存在性,证明主要是利用了能量方法. 相似文献
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Huan Liu 《Applicable analysis》2013,92(13):2378-2399
In this paper, we consider an initial-boundary value problem for a sixth-order parabolic equation. We use the modified method of potential wells to study the relationship which the equation solutions existence, blow-up and the asymptotic behavior with initial conditions. 相似文献
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M.B. Erdoğan T.B. Gürel N. Tzirakis 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(7):1947-1973
We study the initial-boundary value problem for the derivative nonlinear Schrödinger (DNLS) equation. More precisely we study the wellposedness theory and the regularity properties of the DNLS equation on the half line. We prove almost sharp local wellposedness, nonlinear smoothing, and small data global wellposedness in the energy space. One of the obstructions is that the crucial gauge transformation we use replaces the boundary condition with a nonlocal one. We resolve this issue by running an additional fixed point argument. Our method also implies almost sharp local and small energy global wellposedness, and an improved smoothing estimate for the quintic Schrödinger equation on the half line. In the last part of the paper we consider the DNLS equation on and prove smoothing estimates by combining the restricted norm method with a normal form transformation. 相似文献
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G. I. Shishkin 《Computational Mathematics and Mathematical Physics》2009,49(10):1748-1764
The initial-boundary value problem in a domain on a straight line that is unbounded in x is considered for a singularly perturbed reaction-diffusion parabolic equation. The higher order derivative in the equation
is multiplied by a parameter ɛ2, where ɛ ∈ (0, 1]. The right-hand side of the equation and the initial function grow unboundedly as x → ∞ at a rate of O(x
2). This causes the unbounded growth of the solution at infinity at a rate of O(Ψ(x)), where Ψ(x) = x
2 + 1. The initialboundary function is piecewise smooth. When ɛ is small, a boundary and interior layers appear, respectively,
in a neighborhood of the lateral part of the boundary and in a neighborhood of the characteristics of the reduced equation
passing through the discontinuity points of the initial function. In the problem under examination, the error of the grid
solution grows unboundedly in the maximum norm as x → ∞ even for smooth solutions when ɛ is fixed. In this paper, the proximity of solutions of the initial-boundary value problem
and its grid approximations is considered in the weighted maximum norm ∥·∥
w
with the weighting function Ψ−1(x); in this norm, the solution of the initial-boundary value problem is ɛ-uniformly bounded. Using the method of special grids
that condense in a neighborhood of the boundary layer or in neighborhoods of the boundary and interior layers, special finite
difference schemes are constructed and studied that converge ɛ-uniformly in the weighted norm. It is shown that the convergence
rate considerably depends on the type of nonsmoothness in the initial-boundary conditions. Grid approximations of the Cauchy
problem with the right-hand side and the initial function growing as O(Ψ(x)) that converge ɛ-uniformly in the weighted norm are also considered. 相似文献
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The initial-boundary value problem for the KdV equation on a finite interval is analyzed in terms of a singular Riemann–Hilbert problem for a matrix-valued function in the complex k-plane which depends explicitly on the space–time variables. For an appropriate set of initial and boundary data, we derive the k-dependent “spectral functions” which guarantee the uniqueness of Riemann–Hilbert problem's solution. The latter determines a solution of the initial-boundary value problem for KdV equation, for which an integral representation is given. To cite this article: I. Hitzazis, D. Tsoubelis, C. R. Acad. Sci. Paris, Ser. I 347 (2009). 相似文献
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A. M. Denisov 《Computational Mathematics and Mathematical Physics》2011,51(9):1588-1595
An initial-boundary value problem for the diffusion equation with an unknown initial condition is considered. Additional information
used for determining the unknown initial condition is an external volume potential whose density is the Laplacian calculated
for the solution of the initial-boundary value problem. Uniqueness theorems for the inverse problem are proved in the case
when the spatial domain of the initial-boundary value problem is a spherical layer or a parallelepiped. 相似文献
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We study the initial-boundary value problem for the one dimensional EulerBoltzmann equation with reflection boundary condition. For initial data with small total variation, we use a modified Glimm scheme to construct the global approximate solutions(U_(△t,d), I_(△t,d)) and prove that there is a subsequence of the approximate solutions which is convergent to the global solution. 相似文献
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带阻尼项的Euler方程组初边值问题的整体解 总被引:2,自引:0,他引:2
本文研究了一维带阻尼项的Euler方程组初边值问题的齐次Dirichlet边值情形.当初值在平衡解附近小扰动时,本文得到了时间整体解的存在唯一性,而且当时间趋于无穷时,此解趋于平衡解. 相似文献
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We establish necessary and sufficient conditions on the boundary function under which a generalized solution to the initial-boundary value problem for the wave equation with boundary conditions of the first kind belongs to W p 1 . 相似文献
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本文研究带有五次项的非线性Schrödinger方程初边值问题的有限差分法,其中方程中二阶偏导数项的系数、五次项的系数及初值满足下面的条件(1.6).针对此问题,我们研究了一个守恒差分格式,在条件(1.6)下,差分解的$L^{\infty}$模先验估计被得到.在此基础上,我们得到了差分解最优$L^2$模的误差估计. 相似文献
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本文讨论下面方程的初边值问题。光滑有界区域,且p>2.本文用正则化方法证明了当p>α+2时广义解的全局存在性,对p<α+2的情形,证明当初值u_o(x)属于一稳定集W时广义解的全局存在性,而当u_o(x)充分大时广义解只局部存在并在有限时间内爆破。最后用共轭算子法得到了广义解的唯一性定理。 相似文献