A strong uniqueness theorem for planar vector fields

This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.Dedicated to Constantine Dafermos on his 60^th birthdayWork supported in part by CNPq, FINEP, FAPESP and a Research Incentive Fund grant of Temple University.     

Finite element analysis of thermally coupled nonlinear Darcy flows

We consider a coupled system describing nonlinear Darcy flows with temperature dependent viscosity and with viscous heating. We first establish existence, uniqueness, and regularity of the weak solution of the system of equations. Next, we decouple the coupled system by a fixed point algorithm and propose its finite element approximation. Finally, we present convergence analysis with an error estimate between continuous solution and its iterative finite element approximation.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Carleman Estimates for Second-Order Hyperbolic Equations

In the space of variables (x, t) ∈ ? ⁿ⁺¹, we consider a linear second-order hyperbolic equation with coefficients depending only on x. Given a domain D ? ? ⁿ⁺¹ whose projection to the x-space is a compact domain Ω, we consider the question of construction of a stability estimate for a solution to the Cauchy problem with data on the lateral boundary S of D. The well-known method for obtaining such estimates bases on the Carleman estimates with an exponential-type weight function exp(2τ?(x, t)) whose construction faces certain difficulties in case of hyperbolic equations with variable coefficients. We demonstrate that if D is symmetric with respect to the plane t = 0 then we can take ?(x, t) to be the function ?(x, t) = s ²(x, x ⁰) ? pt ², where s(x, x ⁰) is the distance between points x and x ⁰ in the Riemannian metric induced by the differential equation, p is some positive number less than 1, and the fixed point x ⁰ can either belong to the domain Ω or lie beyond it. As for the metric, we suppose that the sectional curvature of the corresponding Riemannian space is bounded above by some number k ₀ ≥ 0. In case of space of nonpositive curvature the parameter p can be taken arbitrarily close to 1; in this case as p → 1 the stability estimates lead to a uniqueness theorem which describes exactly the domain of the solution continuation through S. It turns out that, in case of space of bounded positive curvature, construction of a Carleman estimate is possible only if the product of k ₀ and sup _x∈Ω s ²(x, x ⁰) satisfies some smallness condition.     

奇异非线性二阶三点边值问题正解的存在唯一性

本文研究了一类奇异非线性二阶三点边值问题，通过摄动技巧和比较原理获得了所论问题正解的存在唯一性。     

含两组状态变量等变分歧问题开折的唯一性和稳定性

基于奇点理论中光滑映射芽的接触等价,讨论多参数等变分歧问题关于接触等价的开折的唯一性和稳定性.将这种等变分歧问题的状态变量分为两组,其中一组的诸状态变量可以独立地变化,而属于另一组的诸状态变量在变化过程中依赖于前一组中的诸状态变量.得出了在接触等价下,满足一定条件的等变分歧问题的万有开折是唯一的,并且给出了一定条件下等变分歧问题开折稳定的一个充要条件.     

GLOBAL L^p ESTIMATES FOR THE PARABOLIC EQUATION OF THE BI-HARMONIC TYPE

In this paper similarly to the second-order case, we give an elementary and straightforward proof of global Lp estimates for the initial-value parabolic problem of the bi-harmonic type. Moreover, we obtain the existence and uniqueness of the solutions in the suitable space using the potential theory, Marcinkiewicz interpolation theorem and approximation argument. Meanwhile, by the same approach we can deal with the general polyharmonic cases.     

Well‐posedness of the equations governing the motions of a one‐dimensional hybrid thermo‐elastic structure

In this paper a model for the vibrations of a one‐dimensional hybrid thermo‐elastic structure consisting of an extensible thermo‐elastic beam which is hinged at one end, with a rigid body attached to its free end, is studied with a view to establishing the existence of a unique solution in a weak sense. The model takes account of the effect of stretching on bending and rotational inertia. By treating eigenvalue problems with the spectral parameter also in the boundary conditions, we are able to employ the method of Faedo–Galerkin approximations. Copyright © 2004 John Wiley & Sons, Ltd.     

The capture into parametric autoresonance

In this work, we show that the capture into parametric resonance may be explained as pitchfork bifurcation in the primary parametric resonance equation. We prove that the solution close to the moment of the capture is descibed by the Painlevé-2 equation. We obtain connection formulae for the asymptotic solution of the primary parametric resonance equation before and after the capture using the matching of asymptotic expansions.     

具非线性对流项扩散方程的源型解

研究主部为热传导算子的拟线性抛物型方程Cauchy问题:u_t=u_(xx) (u~n)_x,(x,t)∈S=R×(0,∞),u(x,0)=δ(x),x∈■在一维情形下源型解的存在性,唯一性,不存在性,解的渐近性和相似源型解等问题.在研究过程中,找到了一个n的临界值,即n_0=3.当0≤n相似文献   

Ⅲ类二次系统极限环的惟一性(Ⅰ)

证明了一般的Ⅲ类二次系统当参数a很小时极限环的大范围惟一性,对于一般的参数值a,在适当的条件下也证明了极限环的大范围惟一性.文中也给出了极限环随参数d变化时产生和消失的过程.