共查询到20条相似文献,搜索用时 88 毫秒
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热传导(对流-扩散)方程源项识别的粒子群优化算法 总被引:1,自引:0,他引:1
提出了利用粒子群优化(PSO)算法反演热传导方程与对流-扩散方程源项的一种新方法,在已有文献方法的基础上,求解出这两类方程正问题的解析解,再把源项识别问题转化为最优化问题,结合粒子群优化算法寻优求解.通过数值模拟与统计检验,结果表明,此方法可快速有效地实现热传导方程与对流-扩散方程源项的识别,并可推广应用到其它数学物理方程的源项或参数的反演识别. 相似文献
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《中国科学:数学》2015,(7)
本文对纳米材料力学性质定量分析中出现的反问题理论、计算和应用进行了探讨.这类问题在纳米材料科学以及功能器件开发等方面中有着重要的应用,对纳米尺度下的测量、优化设计、研发及应用有着重大的指导意义.根据工程测量方法的不同,纳米材料力学性质的定量分析方法一般可以分为两类,静态法和动态法.本文针对两种方法,率先研究Euler-Bernoull方程的反演随机源项、反演系数和反谱问题,得到了对于一般非均匀纳米材料性质测定的方法,其中对于反演随机源项,本文得到在依概率意义下的收敛性;对于反谱问题,本文将其转化为优化问题求解,并给出数值算例验证.最后提出这些反问题新的应用和数学上新的研究方向. 相似文献
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时间分数次扩散方程中反演源项问题是一类经典不适定问题.本文构造了一种新的迭代格式作为正则化方法,给出了先验和后验参数选取下相应的收敛性分析.数值算例验证该方法的有效性. 相似文献
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主要考察弹性薄板在规则外力作用下的振动模型.在给定外力源项随时间变化模式的情况下,通过对薄板局部区域一段时间的振动位移观测数据,来反演外力大小的问题,也就是通常所谓的弹性薄板反源问题.给出了弹性薄板反源解的唯一性定理,并推导出板方程的基本解.取基本解方法和Tikhonov正则化方法的精髓,在简谐模式源项作用的情况下,构造了一套算法来反解源项.对Euler-Bernoulli杆和Kirchhoff-Love板的数值算例表明,无论源项是否光滑,测量是否带有误差,基本解方法都因其较好的计算效果,有着广泛的适用性. 相似文献
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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
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本主考虑在边界脉冲源激发下,二维波动方程的势函数反演问题.利用并间测量数据及地表测量数据重建势函数q(x,z),利用反演问题的算子方程形式,通过Frechet导数及对时间卷积的方法,得到了重建q(x,z)的迭代方法. 相似文献
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New Class of Kirchhoff Type Equations with Kelvin-Voigt Damping and General Nonlinearity: Local Existence and Blow-up in Solutions 下载免费PDF全文
Hanni Dridi & Khaled Zennir 《偏微分方程(英文版)》2021,34(4):313-347
In this paper, we consider a class of Kirchhoff equation, in the presence of a Kelvin-Voigt type damping and a source term of general nonlinearity forms. Where the studied equation is given as follows\begin{equation*}u_{tt} -\mathcal{K}\left( \mathcal{N}u(t)\right)\left[ \Delta_{p(x)}u +\Delta_{r(x)}u_{t}\right]=\mathcal{F}(x, t, u).\end{equation*}Here, $\mathcal{K}\left( \mathcal{N}u(t)\right)$ is a Kirchhoff function, $\Delta_{r(x)}u_{t}$ represent a Kelvin-Voigt strong damping term, and $\mathcal{F}(x, t, u)$ is a source term. According to an appropriate assumption, we obtain the local existence of the weak solutions by applying the Galerkin's approximation method. Furthermore, we prove a non-global existence result for certain solutions with negative/positive initial energy. More precisely, our aim is to find a sufficient conditions for $p(x), q(x), r(x), \mathcal{F}(x,t,u)$ and the initial data for which the blow-up occurs. 相似文献
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Shun-Tang Wu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,63(1):65-106
In this paper, a viscoelastic equation with nonlinear boundary damping and source terms of the form $$\begin{array}{llll}u_{tt}(t)-\Delta u(t)+\displaystyle\int\limits_{0}^{t}g(t-s)\Delta u(s){\rm d}s=a\left\vert u\right\vert^{p-1}u,\quad{\rm in}\,\Omega\times(0,\infty), \\ \qquad\qquad\qquad\qquad\qquad u=0,\,{\rm on}\,\Gamma_{0} \times(0,\infty),\\ \dfrac{\partial u}{\partial\nu}-\displaystyle\int\limits_{0}^{t}g(t-s)\frac{\partial}{\partial\nu}u(s){\rm d}s+h(u_{t})=b\left\vert u\right\vert ^{k-1}u,\quad{\rm on} \ \Gamma_{1} \times(0,\infty) \\ \qquad\qquad\qquad\qquad u(0)=u^{0},u_{t}(0)=u^{1},\quad x\in\Omega, \end{array}$$ is considered in a bounded domain ??. Under appropriate assumptions imposed on the source and the damping, we establish both existence of solutions and uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function g, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function g. Moreover, for certain initial data in the unstable set, the finite time blow-up phenomenon is exhibited. 相似文献
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Consider the 1+1-dimensional quasi-linear diffusion equations with convection and source term u t =[ u m ( u x ) n ] x + P ( u ) u x + Q ( u ) , where P and Q are both smooth functions. We obtain conditions under which the equations admit the Lie Bäcklund conditional symmetry with characteristic η= u xx + H ( u ) u 2 x + G ( u )( u x )2− n + F ( u ) u 1− n x and the Hamilton–Jacobi sign-invariant J = u t + A ( u ) u n +1 x + B ( u ) u x + C ( u ) which preserves both signs, ≥0 and ≤0, on the solution manifold. As a result, the corresponding solutions associated with the symmetries are obtained explicitly, or they are reduced to solve two-dimensional dynamical systems. 相似文献
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我们考虑了一类原型为$$\begin{cases}u_t-\Delta u=\overrightarrow{b}(x,t)\cdot\nabla u+\gamma|\nabla u|^2-\text{div}{\overrightarrow{F}(x,t)}+f(x,t), &(x,t)\in \Omega_T,\\ u(x,t)=0,&(x,t)\in\Gamma_T,\\ u(x,0)=u_0(x), &x\in\Omega,\end{cases}$$的一类抛物方程. 其中, 函数$|\overrightarrow{b}(x,t)|^2,|\overrightarrow{F}(x,t)|^2,f(x,t)$位于空间$L^r{(0,T;L^q(\Omega))}$, $\gamma$是一个正常数. 在源项和梯度的系数项在空间$L^r{(0,T;L^q(\Omega))}$具有合适的可积条件下, 本文的目的在于证明先验的$L^\infty$估计以及方程存在有界解. 主要的方法包括通过正则化建立扰动问题, 用非线性的检验函数实现Stampacchia迭代技术以及极限过程中的紧性论断. 相似文献
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We study the scalar conservation law with a noisy nonlinear source, namely,u
l + f(u)x = h(u, x, t) + g(u)W(t), whereW(t) is the white noise in the time variable, and we analyse the Cauchy problem for this equation where the initial data are assumed
to be deterministic. A method is proposed to construct approximate weak solutions, and we then show that this yields a convergent
sequence. This sequence converges to a (pathwise) solution of the Cauchy problem. The equation can be considered as a model
of deterministic driven phase transitions with a random perturbation in a system of two constituents. Finally we show some
numerical results motivated by two-phase flow in porous media.
This research has been supported by VISTA (a research cooperation between the Norwegian Academy of Science and Letters and
Den norske stats oljeselskap, Statoil) and NAVF (the Norwegian Research Council for Science and the Humanities). 相似文献
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不连续三阶两点边值问题的可解性 总被引:4,自引:0,他引:4
证明了非线性三阶两点边值问题u′″(t)-q(u″(t))f(t,u(t)),u(O)=a,u(1)=b,u″(0)=c解的一个存在定理.在这个问题中,f(t,u)是一个Carathéodory函数而边界条件是非齐次的.我们的结论表明该问题能够有一个解,只要在R。的某个有界集合上q(υ)的“本性高度”与f(t,u)的“最大高度”积分的乘积是适当的. 相似文献
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研究三维微分系统:u′1=a1(t)|u2|λ1sgn u2,u′2=a2(t)|u3|λ2sgn u3,u′3=-a3(t)|u1|λ3sgn u1.假设λi(i=1,2,3)是正的常数,ai(t)(i=1,2,3)在区间[0,∞)上是正的连续函数,根据u的分量ui的特殊渐近条件定义了正值解的几种类型。系统满足条件∫0∞ai(t)dt=∞,i=1,2. 相似文献
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一类奇异半线性热方程初值问题解 的唯一性结果 总被引:6,自引:0,他引:6
设u(t,x),u(t,x)为初值问题在带形域ST=(0,T)×Rn内的两个非负经曲解,f(x)连续有界非负的实函数,则有如下的结果:(1)若f(x)不恒为零,则在ST中u(t,x);(2)若γ>1,则在ST中u(t,x)u(t,x);(3)若0>γ>1,f(x)0,则问题(1.1),(1.2)的解不唯一且它的所有非平凡解的集合为u(t,s)=这里s≥0是参数,其中记号(γ)+=max{γ,0}. 相似文献
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A coupled non-linear hyperbolic-sobolev system 总被引:1,自引:0,他引:1
Richard E. Ewing 《Annali di Matematica Pura ed Applicata》1977,114(1):331-349
Summary A boundary-initial value problem for a quasilinear hyperbolic system in one space variable is coupled to a boundary-initial
value problem for a quasilinear equation of Sobolev type in two space variables of the form Mut(x, t)+L(t) u (x, t)=f(x, t, u(x, t)) where M and L(t) are second order elliptic spacial operators. The coupling occurs through
one of the boundary conditions for the hyperbolic system and the source term in the equation of Sobolev type. Such a coupling
can arise in the consideration of oil flowing in a fissured medium and out of that medium via a pipe. Barenblatt, Zheltov,
and Kochina[2] have modeled flow in a fissured medium via a special case of the above equation. A local existence and uniqueness theorem
is demonstrated. The proof involves the method of characteristics, some applications of results of R. Showalter and the contraction
mapping theorem.
Entrata in Redazione il 28 luglio 1976. 相似文献
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利用拓扑度理论和不动点指数理论,研究了二阶非线性变系数奇异微分方程u″(t)+a(t)u(t)=r(t)f(u(t))的周期解的存在性.特别地,本文没有假设a(t)和f(u)的非负性. 相似文献