共查询到20条相似文献,搜索用时 0 毫秒
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L.W White 《Journal of Mathematical Analysis and Applications》1981,82(1):284-291
Boundary control of a pseudoparabolic problem is studied. The trace of a solution y(T; ?) corresponding to a control ? is shown to belong to and continuity properties are established. Two concrete examples are considered and regularity properties of the optimal control are determined in each case. 相似文献
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Solvability analysis of mixed boundary value problems for pseudoparabolic systems in a special scale of weighted Sobolev spaces is presented. The class under consideration contains the linearized Navier-Stokes system. It is proved that, choosing the power weight, one can diminish the number of solvability conditions and in some cases obtain unconditional solvability of the boundary value problems. 相似文献
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S. N. Glazatov 《Siberian Mathematical Journal》2007,48(2):214-228
We prove existence and uniqueness of a weak solution to the first initial-boundary value problem for some class of quasilinear pseudoparabolic equations in nontube domains. Also, we study unique solvability in these domains for the variational inequality connected with the above class of equations. 相似文献
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《Nonlinear Analysis: Theory, Methods & Applications》2007,66(1):179-191
We consider initial boundary value problems for a third-order nonlinear pseudoparabolic equation with one space dimension. The boundary condition is given by an integral; the function involved could exhibit singularities, which distinguishes this nonlocal condition from its Dirichlet or Neumann counterparts. By means of appropriate elliptic estimates we are able to seek solutions not only in the weighted spaces but also in the usual Sobolev spaces. The procedure is carried out in a unified way. Our results characterize a regularity of the pseudoparabolic operator that is different from that of the parabolic operator. 相似文献
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L. W. White 《Journal of Optimization Theory and Applications》1982,36(2):277-288
The feedback operator of a linear pseudoparabolic problem with quadratic criterion is obtained by decoupling of the optimality condition. The feedback operator is shown to be related to the solution of a Riccati equation formulated in theB*-algebra of bounded linear operators onL
2(). This approach shows that the linear feedback operator may be considered as a bounded operator fromL
2() intoH
0
1
(). Finally, we give a theorem establishing the convergence behavior for the feedback operators for these problems as they formally approach an analogous problem of parabolic type.This work was supported in part by the National Science Foundation, Grant No. MCS-7902037. 相似文献
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Alexey Bykov Alexander Panin Alena Sharlo 《Mathematical Methods in the Applied Sciences》2017,40(6):1949-1963
An asymptotic expansion of the contrasting structure‐like solution of the generalized Kolmogorov–Petrovskii–Piskunov equation is presented. A generalized maximum principle for the pseudoparabolic equations is developed. This, together with the generalized differential inequalities method, allows to prove the consistence and convergence of the asymptotic series method. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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利用初值问题解的性态研究了三阶伪抛物型方程边值问题解存在与唯一性问题,给出其解存在唯一的充分条件,同时推广了Elcart and Sigillito的有关结果. 相似文献
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Abdelfatah Bouziani 《Journal of Mathematical Analysis and Applications》2004,291(2):371-386
In this paper, we deal with a class of pseudoparabolic problems with integral boundary conditions. We will first establish an a priori estimate. Then, we prove the existence, uniqueness and continuous dependence of the solution upon the data. Finally, some extensions of the problem are given. 相似文献
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Pseudoparabolic equations in periodic media are homogenized to obtain upscaled limits by asymptotic expansions and two-scale convergence. The limit is characterized and convergence is established in various linear cases for both the classical binary medium model and the highly heterogeneous case. The limit of vanishing time-delay parameter in either medium is included. The double-porosity limit of Richards' equation with dynamic capillary pressure is obtained. 相似文献
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NONLINEAR PSEUDOPARABOLIC EQUATIONS IN ARBITRARY DIMENSIONS 总被引:2,自引:0,他引:2
1.IntroductionAsiswellknownthenonlinearpseudoparabolicequationsweresuggestedandstudiedinconnectionwithmanypracticalproblemsatthebeginningofthe1970s.AmongthemtheBBMequationat box~abet~0(1'1)isthemostimportant,itwassuggestedinconnectionwiththepropagationoflongwavesinnonlineardispersivesystemsbyT.B.Benjaminetallljin1972.In1977,L.A.Medeirosetall2]studiedtheweaksolutionoftheinitialboundaryvalueproblemforageneralizedformof(1.1)RevisedJanuary,25,1995.*ThisworkissupportedbytheNationalScienceFOun… 相似文献
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《Journal of Mathematical Analysis and Applications》2019,469(1):44-75
Multiscale analysis of a degenerate pseudoparabolic variational inequality, modelling the two-phase flow with dynamical capillary pressure in a perforated domain, is the main topic of this work. Regularisation and penalty operator methods are applied to show the existence of a solution of the nonlinear degenerate pseudoparabolic variational inequality defined in a domain with microscopic perforations, as well as to derive a priori estimates for solutions of the microscopic problem. The main challenge is the derivation of a priori estimates for solutions of the variational inequality, uniformly with respect to the regularisation parameter and to the small parameter defining the scale of the microstructure. The method of two-scale convergence is used to derive the corresponding macroscopic obstacle problem. 相似文献
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We construct and analyze splitting schemes for a pseudoparabolic equation. We suggest a three-level vector additive scheme in which part of the time derivatives is taken from the previous time level. Unconditional stability estimates for the splitting schemes are proved. 相似文献
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An analogue of the Galyorkin method for finding approximate solutions to pseudoparabolic equations is proposed and the convergence
of these approximations to the generalized solution belonging to the class L2(Q) is demonstrated. Bibliography: 6 titles.
Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 76, 1992, pp. 18–23. 相似文献
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M. Meyvaci 《Journal of Mathematical Analysis and Applications》2009,352(2):629-633
We obtain sufficient conditions for the blow up of solutions of the initial-boundary value problem for nonlinear pseudoparabolic equation involving nonlinear convective term. 相似文献
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