共查询到19条相似文献,搜索用时 93 毫秒
1.
本文研究了一类竞争型反应扩散方程的时间最优控制问题的存在性问题.利用上下解的方法,得到了反应扩散方程正解的存在性.利用Kakutani不动点定理,证明了反应扩散方程关于正轨迹的局部精确能控性,并据此证明了时间最优控制的存在性. 相似文献
2.
本文讨论了四对谱问题、相应保谱发展方程族以及它们 Lax表示的等价性 ,并利用这种等价关系导出了一些方程的 Lax表示 . 相似文献
3.
利用Mawhin重合度拓展定理, 研究一类具有排斥型奇性的中立型Li\''{e}nard方程周期问题. 在强奇性条件下, 获得周期正解存在性的新结果. 本文允许方程在无穷远点具有不定型奇性, 改进了已有文献中的相关结论. 相似文献
4.
考 虑具有未 知源项的 某些非 线性伪 抛物 型方程 的反演 问题. 首先 将伪抛 物型 方程初 边值问 题化为非线 性发展方 程 Couch y 问题,然 后,利用半 群理论,论 证发展 方程反问 题解的存 在唯一 性,最后, 利用不 动点方法得到 伪抛物型方程反 问题的可解性 相似文献
5.
研究一类非线性拟抛物方程的柯西问题.首先利用与原方程等价的积分方程以及压缩映像原理得到了问题的局部W~(k,p)解的存在性,而后在某些假设下得到了问题W~(k,p)解的整体存在性,最后利用凸性方法得到了解的有限时间内爆破. 相似文献
6.
7.
讨论了具有第三类非线性边界条件的非线性发展方程的混合问题,并在已知函数满足某些假设的条件下,利用抛物型方程的最大值原理和凸性方法,证明了该问题的解在有限时间内爆破. 相似文献
8.
该文分析一族含有依赖时间参数t线性算子的时间分数阶非自治发展方程,利用Lions表示定理,得到了弱解适定性的充分条件;基于正交投影,建立了时间分数阶发展方程弱解的不变性准则.该文所研究方程中的算子是依赖时间的. 相似文献
9.
何跃 《数学年刊A辑(中文版)》2004,(2)
本文考虑一类二阶退化半线性椭圆型方程边值问题.由椭圆正则化方法建立能量不等式,利用紧性推理,Banach—Saks定理,弱解与强解一致性,解常微分方程,椭圆型方程正则性定理,迭代方法.极值原理和Fredholm—Riesz-Schauder理论,可得相应线性问题适定性及解的高阶正则性;再由Moser引理和Banach不动点定理可得半线性问题解的存在性.这类问题与几何中无穷小等距形变刚性问题密切相关,其高阶正则性解的存在性对几何应用尤为重要. 相似文献
10.
11.
12.
The problem related to controlled potential experiments in electrochemistry is studied. Ion transport is regarded as the superposition of diffusion and migration. Modelling of the experiment leads to a problem for a nonlinear parabolic equation with additional condition. Driven by the needs of theoretical analysis, from the point of view a inverse coefficient problem, we analyze the monotonicity of input-output mappings in inverse coefficient and source problems for this parabolic equation. Additionally, we extend the nonlinear parabolic equation to a more general case. Under some proper conditions, we investigate the existence of quasisolution of the generalized nonlinear parabolic equation. 相似文献
13.
In this article, we present an inverse problem for the nonlinear 1D Kuramoto–Sivashinsky (KS) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a part of the boundary and also at some positive time in the whole space domain. The Lipschitz stability for this inverse problem is our main result and it relies on the Bukhge?m–Klibanov method. The proof is indeed based on a global Carleman estimate for the linearized KS equation. 相似文献
14.
E. V. Tabarintseva 《Numerical Analysis and Applications》2018,11(3):236-255
An inverse boundary value problem for a nonlinear parabolic equation is considered. Two-sided estimates for the norms of values of a nonlinear operator in terms of those of a corresponding linear operator are obtained.On this basis, two-sided estimates for the modulus of continuity of a nonlinear inverse problem in terms of that of a corresponding linear problem are obtained. A method of auxiliary boundary conditions is used to construct stable approximate solutions to the nonlinear inverse problem. An accurate (to an order) error estimate for the method of auxiliary boundary conditions is obtained on a uniform regularization class. 相似文献
15.
We prove a theorem on the local controllability of a system described by a nonlinear evolution equation in Banach space when the control is a multiplier on the right-hand side. We obtain sufficient conditions on the size of the neighborhood from which we can take the function from the overdetermination condition so that the inverse problem is uniquely solvable. 相似文献
16.
P. P. Kulish 《Journal of Mathematical Sciences》1983,21(5):718-723
For linear problems which are associated with known, exactly integrable nonlinear evolution equations, one gives the corresponding integrodifferential Λ-operators. Relative to the expansions with respect to the elgenfunctions of Λ-operators, the method of the inverse scattering problem can be considered as the analog of the Fourier transform of linear problems, while the Λ-operators are the analogues of the differentiation operator. One considers the equations: Koteweg-de Vries, the nonlinear Schrödinger equations, the nonlinear Schrödinger equations with a derivative, the system of three waves, the matricial analog of the KdV equation, the Toda chain equation. 相似文献
17.
S. A. Buterin 《Differential Equations》2010,46(1):150-154
We consider the sum of the Sturm-Liouville operator and a convolution operator. We study the inverse problem of reconstructing
the convolution operator from the spectrum. This problem is reduced to a nonlinear integral equation with a singularity. We
prove the global solvability of this nonlinear equation, which permits one to show that the asymptotics of the spectrum is
a necessary and sufficient condition for the solvability of the inverse problem. The proof is constructive. 相似文献
18.
微分特征列法用于拟微分算子和非线性发展方程Lax表示的计算.首先,利用微分特征列法和微分带余除法计算拟微分算子的逆和方根,由于不必求解常微分方程组,并将解代入,因此,使得计算得以简化.其次,利用微分特征列法,约化从广义Lax方程和Zakharov-Shabat推出的非线性偏微分方程,并得到相应的非线性发展方程.在Mathematica计算机代数系统上,编写了相关程序,从而可以利用计算机辅助完成一些非线性发展方程Lax表示的计算. 相似文献
19.
Yan-Chow Ma 《Studies in Applied Mathematics》1984,70(3):201-213
The evolution equation for the nonlinear Kelvin-Helmholtz wave envelope with its carrier wavenumber near direct resonance is formulated directly by using the nonlinear dispersion relation. The stability of a wavetrain is examined, and the long-time evolution for an arbitrary initial condition is studied through inverse scattering transforms. 相似文献