共查询到20条相似文献,搜索用时 15 毫秒
1.
A discrepancy principle for solving nonlinear equations with monotone operators given noisy data is formulated. The existence and uniqueness of the corresponding regularization parameter a(δ) are proved. Convergence of the solution obtained by the discrepancy principle is justified. The results are obtained under natural assumptions on the nonlinear operator. 相似文献
2.
Carmen Calvo-Jurado 《Journal of Mathematical Analysis and Applications》2005,306(1):282-316
We study the asymptotic behaviour of the solutions of linear parabolic Dirichlet problems when the coefficients and the domains where the problems are posed vary simultaneously. In the limit problem it appear the H-limit of the operators, and as it is usual in the homogenization of Dirichlet problems, a new term of order zero. We also obtain a corrector result. 相似文献
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4.
Ryuichi Suzuki 《Journal of Differential Equations》2003,190(1):150-181
The Cauchy problem
(P) 相似文献
5.
Liselott Flodén Anders Holmbom Marianne Olsson Nils Svanstedt 《Annali dell'Universita di Ferrara》2007,53(2):217-232
Reiterated homogenization is studied for divergence structure parabolic problems of the form . It is shown that under standard assumptions on the function a(y
1,y
2,t,ξ) the sequence of solutions converges weakly in to the solution u of the homogenized problem .
相似文献
6.
Xiaoyu Fu 《Journal of Functional Analysis》2009,257(5):1333-851
The paper is devoted to a study of the null controllability for the semilinear parabolic equation with a complex principal part. For this purpose, we establish a key weighted identity for partial differential operators (with real functions α and β), by which we develop a universal approach, based on global Carleman estimate, to deduce not only the desired explicit observability estimate for the linearized complex Ginzburg-Landau equation, but also all the known controllability/observability results for the parabolic, hyperbolic, Schrödinger and plate equations that are derived via Carleman estimates. 相似文献
7.
This is a subsequent work of our previous one in [25]. Let the nonlinear terms of non-autonomous parabolic problems with singular initial data satisfy subcritical and critical growth conditions. We first establish the existence of uniform attractors in W1,r(Ω), 1<r<N, for the family of processes corresponding to the equations with external forces being translation bounded but not translation compact. Then, we prove the existence of pullback attractors in Lr(Ω) and W1,r(Ω), respectively, for the process corresponding to the equation with the weaker assumption on the external force than previous one. Finally, we investigate the robust of attractors and establish the existence of pullback exponential attractors for the process acting in Lr(Ω) and W1,r(Ω), respectively. 相似文献
8.
This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation. The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients. 相似文献
9.
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative coefficients). We propose to consider a class of methods that allows us to evaluate all time-dependent operators at real values of the time, leading to schemes which are stable and simple to implement. If the system can be considered as the perturbation of an exactly solvable problem and the flow of the dominant part is advanced using real coefficients, it is possible to build highly efficient methods for these problems. We show the performance of this class of methods on several numerical examples and present some new improved schemes. 相似文献
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11.
V. BisogninG. Perla Menzala 《Applied Mathematics Letters》1994,7(6):81-84
We study the asymptotic behaviour in time of the solutions of a class of evolution equations whose simplest representative would be the Korteweg de Vries equation with variable coefficients. Specific rates of decay are given in either the “conservative” or the dissipative case. 相似文献
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14.
Quantitative estimates of unique continuation for parabolic equations and inverse initial-boundary value problems with unknown boundaries 总被引:4,自引:0,他引:4
B. Canuto E. Rosset S. Vessella 《Transactions of the American Mathematical Society》2002,354(2):491-535
In this paper we obtain quantitative estimates of strong unique continuation for solutions to parabolic equations. We apply these results to prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in , from the knowledge of overdetermined boundary data for parabolic boundary value problems.
15.
Muhammad Aslam Noor Khalida Inayat Noor Abdelouahed Hamdi Eman H. El-Shemas 《Optimization Letters》2009,3(3):329-335
In this paper, we introduce and consider the problem of finding zeroes of difference of two monotone operators in a Hilbert
space. Using the resolvent operator technique, we show that this problem is equivalent to the fixed point problem. This equivalence
is used to suggest and analyze an iterative method for finding a zero of difference of two monotone operators. We also discuss
the convergence of the iterative method under suitable conditions. Our method of proof is very simple as compared with other
techniques. 相似文献
16.
The ill-posed parabolic equation backward in time
17.
E. M. Abbasov O. A. Dyshin B. A. Suleimanov 《Computational Mathematics and Mathematical Physics》2009,49(9):1554-1566
A method based on wavelet transforms is proposed for finding classical solutions to initial-boundary value problems for second-order
quasilinear parabolic equations. For smooth data, the convergence of the method is proved and the convergence rate of an approximate
weak solution to a classical one is estimated in the space of wavelet coefficients. An approximate weak solution of the problem
is found by solving a nonlinear system of equations with the help of gradient-type iterative methods with projection onto
a fixed subspace of basis wavelet functions. 相似文献
18.
Alemdar Hasanov Ali Demir Arzu Erdem 《Journal of Mathematical Analysis and Applications》2007,335(2):1434-1451
This article presents a mathematical analysis of input-output mappings in inverse coefficient and source problems for the linear parabolic equation ut=(kx(x)ux)+F(x,t), (x,t)∈ΩT:=(0,1)×(0,T]. The most experimentally feasible boundary measured data, the Neumann output (flux) data f(t):=−k(0)ux(0,t), is used at the boundary x=0. For each inverse problems structure of the input-output mappings is analyzed based on maximum principle and corresponding adjoint problems. Derived integral identities between the solutions of forward problems and corresponding adjoint problems, permit one to prove the monotonicity and invertibility of the input-output mappings. Some numerical applications are presented. 相似文献
19.
Boundary controllability of parabolic coupled equations 总被引:1,自引:0,他引:1
Enrique Fernández-Cara Manuel González-Burgos Luz de Teresa 《Journal of Functional Analysis》2010,259(7):1720-1758
This paper is concerned with the boundary controllability of non-scalar linear parabolic systems. More precisely, two coupled one-dimensional parabolic equations are considered. We show that, in this framework, boundary controllability is not equivalent and is more complex than distributed controllability. In our main result, we provide necessary and sufficient conditions for the null controllability. 相似文献
20.
We study asymptotics as of solutions to a linear, parabolic system of equations with time-dependent coefficients in , where is a bounded domain. On we prescribe the homogeneous Dirichlet boundary condition. For large values of t, the coefficients in the elliptic part are close to time-independent coefficients in an integral sense which is described
by a certain function . This includes in particular situations when the coefficients may take different values on different parts of and the boundaries between them can move with t but stabilize as . The main result is an asymptotic representation of solutions for large t. A consequence is that for , the solution behaves asymptotically as the solution to a parabolic system with time-independent coefficients. 相似文献