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一类非线性卷积拟抛物型积分微分方程整体解的存在性问题 总被引:4,自引:0,他引:4
本文研究一类非线性卷积拟抛物型积分微分方程的初边值问题,是运用Galerkin方法结合能量型先验估计证明了其整体强解的存在性、唯一性和正则性,并在一定条件下讨论了整体解的不存在性. 相似文献
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本文证明了广义Ginzburg-Landau型非线性高阶抛物方程的周期边值问题和Canchy问题广义解和古典解的整体存在性和正则性,并且还证明了解的唯一性和这些解的渐近性质. 相似文献
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本文考虑一类多维非线性复抛物型方程组的初边值问题和柯西问题,采用Galerkin方法和紧性原理,证明了这些问题整体强解与整体古典解的存在性、唯一性和正则性。 相似文献
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一类双边退缩抛物型方程的混合问题的广义解的正则性@韩普宪¥许昌教育学院@王向东¥郑州轻工业学院一类双边退缩抛物型方程的混合问题的广义解的正则性韩普宪(许昌教育学院,许昌461000)王向东(郑州轻工业学院,郑州450002)考虑混合问题:(Ⅰ)(c(u))... 相似文献
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证明了二阶完全非线性抛物型方程周期粘性解的存在唯一性,在标准假设下解决了非线性抛物型方程古典周期解的存在唯一性问题。 相似文献
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在自然结构条件下证明了具有初值和非线性斜边值的二阶完全非线性抛物方程障碍问题W~(2.1)_∝强解的存在唯一性. 相似文献
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该文给出了双调和型抛物方程初值问题解的Schauder估计,并且在适当的空间中证明了解的存在性与惟一性.类似于二阶情形,首先通过Fourier变换得到一个形式解,然后再利用位势理论和逼近方法得到解的正则性、唯一性及存在性.该方法简单而易懂. 相似文献
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偏微分方程解的水平集是一个重要研究对象,与偏微分方程解的存在性、唯一性和正则性紧密相关.本文介绍椭圆和抛物方程解的水平集的微观凸性原理. 相似文献
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M. Kubo K. Shirakawa N. Yamazaki 《Journal of Mathematical Analysis and Applications》2012,387(2):490-511
We create a general framework for mathematical study of variational inequalities for a system of elliptic–parabolic equations. In this paper, we establish a solvability theorem concerning the existence of solutions for the vector-valued elliptic–parabolic variational inequality with time-dependent constraint. Moreover, we give some applications of the system, for example, time-dependent boundary obstacle problem and time-dependent interior obstacle problem. 相似文献
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This paper studies parabolic quasiminimizers which are solutions to parabolic variational inequalities. We show that, under a suitable regularity condition on the boundary, parabolic Q-quasiminimizers related to the parabolic p-Laplace equations with given boundary values are stable with respect to parameters Q and p. The argument is based on variational techniques, higher integrability results and regularity estimates in time. This shows that stability does not only hold for parabolic partial differential equations but it also holds for variational inequalities. 相似文献
14.
Xiangdong Wang Xiting Liang Haiwu Rong Caixia Zhang Dept. of Math. Foshan University Foshan Guangdong 《Annals of Differential Equations》2010,(1):59-69
In this paper, a double obstacle problem of variational inequalities is considered and its solutions is obtained. The results of one-sided obstacle problem are not required in the analysis of our main results, which is different from the previous works. 相似文献
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In this work, the contact problem between an elastic body and a rigid obstacle is studied, including the development of material damage which results from internal compression or tension. The variational problem is formulated as a first-kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field. The existence of a unique local weak solution is stated. Then, a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, three two-dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme. 相似文献
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§ 1.Preliminary LetEbeareflexiveBanachspacewithanorm‖·‖ ,E′itsdualspaceand〈· ,·〉thepairbetweenE′andE .SupposethatHisaHilbertspacewiththenorm |·|andinnerproduct (· ,·)suchthatE H E′ ,( 1°)wheretheformersaredenseinthelattersandthecorrespondingidenticalmapsarecont… 相似文献
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This paper deals with the Lipschitz regularity of minimizers for a class of variational obstacle problems with possible occurrence of the Lavrentiev phenomenon. In order to overcome this problem, the availment of the notions of relaxed functional and Lavrentiev gap is needed. The main tool used here is a crucial Lemma which reveals to be needed because it allows us to move from the variational obstacle problem to the relaxed-functional-related one. This is fundamental in order to find the solutions’ regularity that we intended to study. We assume the same Sobolev regularity both for the gradient of the obstacle and for the coefficients. 相似文献
18.
Xiting Liang 《偏微分方程(英文版)》1995,8(2):145-158
The regularity for solutions of elliptic equations is rather perfectly solved. But it does not so perfect for that of elliptic variational inequalities. In literature only different special situations are considered. Now the boundedness, C^{0,λ} continuity and C^{1,α} regularity are proved for solutions of one-sided obstacle problems under more general structural conditions, in which the growth orders of u are permitted to reach the critical exponents and the growth order ϒ of the gradient in D is permitted to be super critical as 1 < p < n. 相似文献
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A parabolic variational inequality is investigated which comes from the study of the optimal exercise strategy for the perpetual American executive stock options in financial markets. It is a degenerate parabolic variational inequality and its obstacle condition depends on the derivative of the solution with respect to the time variable. The method of discrete time approximation is used and the existence and regularity of the solution are established. 相似文献
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In this work, we present a novel power penalty method for the approximation of a global solution to a double obstacle complementarity problem involving a semilinear parabolic differential operator and a bounded feasible solution set. We first rewrite the double obstacle complementarity problem as a double obstacle variational inequality problem. Then, we construct a semilinear parabolic partial differential equation (penalized equation) for approximating the variational inequality problem. We prove that the solution to the penalized equation converges to that of the variational inequality problem and obtain a convergence rate that is corresponding to the power used in the formulation of the penalized equation. Numerical results are presented to demonstrate the theoretical findings. 相似文献