共查询到20条相似文献,搜索用时 15 毫秒
1.
A. V. Glushak 《Mathematical Notes》2005,77(1-2):26-38
The uniform well-posedness of a Cauchy-type problem with two fractional derivatives and bounded operator A is proved. For an unbounded operator A we present a test for the uniform well-posedness of the problem under consideration consistent with the test for the uniform well-posedness of the Cauchy problem for an equation of second order.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 28–41.Original Russian Text Copyright © 2005 by A. V. Glushak.This revised version was published online in April 2005 with a corrected issue number. 相似文献
2.
In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation Au = b. We prove that if A is a quasi-uniformly monotone and hemi-continuous operator, then A?1 is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence of Galerkin approximations to the solution of steady-state electromagnetic p-curl systems.
相似文献3.
S. A. Kuzhev 《Ukrainian Mathematical Journal》1990,42(5):616-618
In a Hilbert space H with indefinite J-metric, the uniform well-posedness of the Cauchy problem is studied for the equation dx/dt=Ax, where A is a maximal J-dissipative operator. In particular, in the case of a Pontryagin space an analog of Phillips's theorem on the relation between the maximal dissipative operator A and the uniform well-posedness of the Cauchy problem is obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 5, pp. 697–700, May, 1990. 相似文献
4.
A. V. Glushak 《Russian Mathematics (Iz VUZ)》2009,53(9):10-19
We prove the uniform correctness of a Cauchy-type problem with two fractional derivatives and a bounded operator A. We propose a criterion for the uniform correctness of unbounded operator A. 相似文献
5.
Shang Quan Bu 《数学学报(英文版)》2010,26(7):1223-1232
We study the well-posedness of the equations with fractional derivative D^αu(t) = Au(t) + f(t),0≤ t ≤ 2π, where A is a closed operator in a Banach space X, α 〉 0 and D^α is the fractional derivative in the sense of Weyl. Using known results on LP-multipliers, we give necessary and/or sufficient conditions for the LP-well-posedness of this problem. The conditions we give involve the resolvent of A and the Rademacher boundedness. Corresponding results on the well-posedness of this problem in periodic Besov spaces, periodic Triebel-Lizorkin spaces and periodic Hardy spaces are also obtained. 相似文献
6.
Shangquan Bu 《Archiv der Mathematik》2010,95(1):63-73
We introduce the (W
1,p
, L
p
)-mild well-posedness for the vector-valued problem u′ = Au + f on the real line
\mathbbR{\mathbb{R}} and give a characterization of this property by the L
p
-multiplier defined by the resolvent of the closed operator A. 相似文献
7.
P. V. Vinogradova 《Differential Equations》2010,46(7):962-972
In the present paper, we consider the Galerkin method for a quasilinear differentialoperator equation with a leading self-adjoint
operator A(t) and a subordinate monotone operator K. For the projection subspaces we take linear spans of eigenelements of an operator similar to the leading operator A(t). We obtain new estimates for the Galerkin method and consider applications to an initial-boundary value problem for a parabolic
equation of higher order. 相似文献
8.
Polina Vinogradova Anatoli Zarubin 《Numerical Functional Analysis & Optimization》2013,34(1-2):148-167
In the current paper, we study a projection method for a Cauchy problem for an operator-differential equation with a leading self-adjoint operator A(t) and a subordinate linear operator K(t) in a Hilbert space. The projection subspaces are linear spans of eigenvectors of an operator similar to A(t). It is assumed that the operators A(t) and K(t) are sufficiently smooth. Error estimates for the approximate solutions and their derivatives are obtained. The application of the developed method for solving the initial boundary value problems is given. 相似文献
9.
P. V. Vinogradova 《Russian Mathematics (Iz VUZ)》2010,54(7):1-11
We study the projection-difference methods for approximate solving the Cauchy problem for operator-differential equations
with a leading self-adjoint operator A(t) and a subordinate linear operator K(t), whose definition domain is independent of t. Operators A(t) and K(t) are assumed to be sufficiently smooth. We obtain estimates for the rate of convergence of approximate solutions to the exact
solution as well as those for fractional degrees of an operator similar to A(0). 相似文献
10.
Mari Grobbelaar‐Van Dalsen 《Mathematical Methods in the Applied Sciences》2003,26(14):1223-1240
This paper is concerned with the stabilization 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. The model takes account of the effect of stretching on bending and rotational inertia. The property of uniform stability of the energy associated with the model is asserted by constructing an appropriate Lyapunov functional for an abstract second order evolution problem. Critical use is made of a multiplier of an operator theoretic nature, which involves the fractional power A?1/2 of the bi‐harmonic operator pair A acting in the abstract evolution problem. An explicit decay rate of the energy is obtained. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
11.
Sofiya Ostrovska 《Numerical Functional Analysis & Optimization》2016,37(4):492-498
The article deals with the following problem: given a bounded linear operator A in a Banach space X, how can multiplication of A by an operator of norm one (contraction) affect the numerical radius of A? The approach used in this work is close to that employed by Vieira and Kubrusly in 2007 for their study concerning spectral radius. It turns out that this study is closely related to the study of V-operators conducted in 2005 by Khatskevich, Ostrovskii, and Shulman; the results of this article demonstrate that in certain cases the obtained property of an operator implies that it is a V-operator, while in some other cases the converse is true. 相似文献
12.
We consider a Cauchy type problem in a Banach space. Under the assumption that the corresponding Cauchy type problem with
the operator A is uniformly well-posed and the operator B(t) is subordinate to A in some sense, we prove the unique solvability of the considered problem and its continuous dependence on initial data. 相似文献
13.
In this paper, we study a Sturm–Liouville operator with eigenparameter‐dependent boundary conditions and transmission conditions at two interior points. By establishing a new operator A associated with the problem, we prove that the operator A is self‐adjoint in an appropriate space H, discuss completeness of its eigenfunctions in H, and obtain its Green function. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
14.
Convergence Rate of Galerkin Method for a Certain Class of Nonlinear Operator-Differential Equations
Polina Vinogradova 《Numerical Functional Analysis & Optimization》2013,34(3):339-365
In this article, we study a Galerkin method for a nonstationary operator equation with a leading self-adjoint operator A(t) and a subordinate nonlinear operator F. The existence of the strong solutions of the Cauchy problem for differential and approximate equations are proved. New error estimates for the approximate solutions and their derivatives are obtained. The developed method is applied to an initial boundary value problem for a partial differential equation of parabolic type. 相似文献
15.
Let −A be a linear, injective operator, on a Banach spaceX. We show that ∃ anH
∞ functional calculus forA if and only if −A generates a bouned strongly continuous holomorphic semigroup of uniform weak bounded variation, if and only ifA(ζ+A)
−1 is of uniform weak bounded variation. This provides a sufficient condition for the imaginary powers ofA, {A−is} sεR, to extend to a strongly continuous group of bounded operators; we also give similar necessary conditions. 相似文献
16.
Let A be an operator from a real Banach space into a real Hilbert space. In this paper we study least squares regularization methods for the ill-posed operator equation A(u) = f using nonlinear nondifferentiable penalty functionals. We introduce a notion of distributional approximation, and use constructs of distributional approximations to establish convergence and stability of approximations of bounded variation solutions of the operator equation. We also show that the results provide a framework for a rigorous analysis of numerical methods based on Euler-Lagrange equations to solve the minimization problem. This justifies many of the numerical implementation schemes of bounded variation minimization that have been recently proposed. 相似文献
17.
In this paper we prove a well-posedness result for the Cauchy problem. We study a class of first order hyperbolic differential
[2] operators of rank zero on an involutive submanifold ofT
*
R
n+1-{0} and prove that under suitable assumptions on the symmetrizability of the lifting of the principal symbol to a natural
blow up of the “singular part” of the characteristic set, the operator is strongly hyperbolic. 相似文献
18.
Christian Le Merdy 《Integral Equations and Operator Theory》2000,37(1):72-94
This paper is devoted to dual operator algebras, that isw
*-closed algebras of bounded operators on Hilbert space. We investigate unital dual operator algebrasA with the following weak* similarity property: for every Hilbert spaceH, anyw
*-continuous unital homomorphism fromA intoB(H) is completely bounded and thus similar to a contractive one. We develop a notion of dual similarity degree for these algebras,
in analogy with some recent work of Pisier on the similarity problem on operator algebras. 相似文献
19.
This article deals with linear operators T on a complex Hilbert space ?, which are bounded with respect to the seminorm induced by a positive operator A on ?. The A-adjoint and A 1/2-adjoint of T are considered to obtain some ergodic conditions for T with respect to A. These operators are also employed to investigate the class of orthogonally mean ergodic operators as well as that of A-power bounded operators. Some classes of orthogonally mean ergodic or A-ergodic operators, which come from the theory of generalized Toeplitz operators are considered. In particular, we give an example of an A-ergodic operator (with an injective A) which is not Cesàro ergodic, such that T ?* is not a quasiaffine transform of an orthogonally mean ergodic operator. 相似文献
20.
A. Ya. Shklyar 《Ukrainian Mathematical Journal》1996,48(7):1131-1139
For the equation y″(t)+Ay′(t)+By(t)=0, where A and B are arbitrary commuting normal operators in a Hilbert space H, we obtain a necessary and sufficient condition for well-posedness of the Cauchy problem in the space of initial data D(B)×(D(A)∩D(|B|1/2)) and for weak well-posedness of the Cauchy problem in H×H_(|A|+|B|1/2+1). This condition is expressed in terms of location of the joint spectrum of the operators A and B in C 2. In terms of location of the spectrum of the operator pencil z 2+Az+B in C 1, such a condition cannot be written. 相似文献