Global Approximately Controllability and Nite Dimensional Exact Controllability for Parabolic Equation

We study the globally approximate controllability and finite-dimensional exact controllability of parabolic equation where the control acts on a mobile subset of Ω,or, a curve in Q =Ω × (0, T).     

Asymptotic Properties for a Semilinear Edge-Degenerate Parabolic Equation

The author deals with a semi-linear edge-degenerate parabolic equation, and proves that the solution increases exponentially under the initial energy J(u₀) ≤ d, where d is the mountain-pass level. Moreover, the author estimates the blow-up time and the blow-up rate for the solution under J(u₀) < 0.     

半线性抛物方程支配系统的最优性条件

本文讨论了控制变量含于高阶导数项系数中的抛物型偏微分方程支配系统的最优控制问题,给出了最优控制的必要条件．     

拟线性抛物型方程解的爆破

本文讨论了一类拟线性抛物型方程具有某种非线性边界条件的解的爆破性质,证明了其解在有限时间T_0~-内爆破。     

On the Approximate Controllability of Some Semilinear Parabolic Boundary-Value Problems

We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem. Accepted 10 June 1996     

Propagation of Perturbations of Solutions for a Doubly Degenerate Nonlinear Parabolic Equation

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一类半线性抛物边值问题的最大值原理

文中构造了一类具有Dirichlet或Neumann边界条件的半线性抛物方程u_t=Δu+f(x,u,q,t) (q=|u|^2)的解的一个辅助函数，对其使用Hopf最大值原理和黎曼几何理论，从而获得了该函数的最大值原理，据此原理获得了梯度q和解u的估计.     

半线性三阶差分方程边值问题的非负解

该文研究了一类半线性三阶差分方程边值问题Δ３ｕ（ｔ）＋ａ（ｔ）ｆ（ｕ（ｔ））＝０,２≤Ｔ≤Ｔ＋２,ｕ（０）＝ｕ（１）＝ｕ（Ｔ＋３）＝０的非负解,得到了该方程在锥与环形域相交部分非负解的存在性,包含、改近和推广了文［３,４,５,６］的主要结果．     

Stabilizing Semilinear Parabolic Equations

In this paper we prove the internal feedback stabilization of steady-state solutions of semilinear parabolic equations and introduce a controller synthesis methodology based on finite element approximations of the original PDEs. Numerical tests are given for some one- and two-dimensional nonlinear parabolic equations.     

Hamiltonian Pontryagin's Principles for Control Problems Governed by Semilinear Parabolic Equations

In this paper we study optimal control problems governed by semilinear parabolic equations. We obtain necessary optimality conditions in the form of an exact Pontryagin's minimum principle for distributed and boundary controls (which can be unbounded) and bounded initial controls. These optimality conditions are obtained thanks to new regularity results for linear and nonlinear parabolic equations. Accepted 17 March 1997     

On Singular Solutions of Boundary Value Problems for Quasilinear Parabolic Equations with Absorption

The existence and nonexistence of non-trivial solutions for the boundary value problemare studied.     

半线性Sobolev方程的H~1-Galerkin混合有限元方法

利用H~1-Galerkin混合有限元方法研究了一维半线性Sobolev方程,得到了半离散解的最优阶误差估计,优点是不需验证LBB相容性条件.     

On a Class of Coupled Variational Formulations for a Nonlinear Parabolic Equation

51.Introducti0nSince198O)stheoriesandapplicationsofboundaryelementmethods(BEM)orboundaryintegralmethods(BIM)havemadegreatsuccessesfortheparaboliclnit1alboundaryvalueproblems(seeL1-12j),andtheapproachhasbeenappliedtonumericalsolutionsofinitialboundaryva1ueproblemssuccessfully(seeL1-5j'L8j).Thepropertiesofboundaryelementoperatorshavebeenstudiedbyboundaryintegralmethodsbymanyauthors(see.[4j,L6J'[7j'L12J).Theseresultsprovideabasisforconvergencesanderrorestimatesfornumericalapproximationofbou…     

一类半线性抛物型方程的紧差分格式

本文构造了一类半线性抛物方程初边值问题的紧差分格式．利用离散能量估计证明了差分格式解的存在唯一性、收敛性和无条件稳定性，并给出了在离散L^∞模意义下收敛阶数为O（h^4＋τ^2）．数值例子验证了理论分析结果。     

半线性问题的瀑布型多重网格法

本文提出了求解半线性椭圆问题的一类新的瀑布型多重网格法，在网格层数固定的条件下证明了此法的最优阶收敛性。     

具有边界摄动的抛物型方程的可解性

本文研究了具有边界摄动的抛物型方程.利用可解性的讨论,得到了原问题的摄动解.     

半线性抛物型方程的双移动边界问题

本文运用Fourier方法和压缩映像不动点原理,证明了半线性抛物型方程的双移动边界问题 u_t=a~2u_(xx) F(x,t,u,u_x),(x,t)∈D_∞, u(l_1(t),t)=0,l_1(0)=0,t∈(0, ∞), u(l_2(t),t)=0,l_2(0)=l_0,t∈(0, ∞), u(x,0)=φ(x),0≤x≤l_0,φ(0)=φ(l_0)=0.解的存在唯一性,其中D_∞={(x,t)|l_1(t)相似文献   

Ground State Solutions for a Semilinear Elliptic Equation Involving Concave-convex Nonlinearities

This work is devoted to the existence and multiplicity properties of the ground state solutions of the semilinear boundary value problem $-Δu=λa(x)u|u|^{q-2}+ b(x)u|u|^{2^∗-2}$ in a bounded domain coupled with Dirichlet boundary condition. Here $2^∗$ is the critical Sobolev exponent, and the term ground state refers to minimizers of the corresponding energy within the set of nontrivial positive solutions. Using the Nehari manifold method we prove that one can find an interval L such that there exist at least two positive solutions of the problem for $λ∈Λ$.     

Scattering for Semilinear Wave Equation with Small Data in High Space Dimensions

In this paper we study the scattering theory for the semilincar wave equation u_{tt} - Δu = F(u(t, x), Du(t, x)) in R^n (n ≥ 4) with smooth and small data. We show that the scattering operator exists for the nonlinear term F = F(λ) = O(|λ|^{1, α}), where α is an integer and satisfies α ≥ 2, n = 4; α ≥ I, n ≥ 5.