共查询到20条相似文献,搜索用时 510 毫秒
1.
S. E. Zhelezovskii 《Computational Mathematics and Mathematical Physics》2010,50(7):1178-1194
The Cauchy problem for a system of two operator-differential equations in Hilbert space that is a generalization of a number
of linear coupled thermoelasticity problems is investigated. Results concerning the high smoothness of the solutions to these
equations are proved. 相似文献
2.
Anatoly N. Kochubei 《Potential Analysis》2012,37(1):1-30
We develop a theory of the Cauchy problem for linear evolution systems of partial differential equations with the Caputo-Dzhrbashyan fractional derivative in the time variable t. The class of systems considered in the paper is a fractional extension of the class of systems of the first order in t satisfying the uniform strong parabolicity condition. We construct and investigate the Green matrix of the Cauchy problem. While similar results for the fractional diffusion equations were based on the H-function representation of the Green matrix for equations with constant coefficients (not available in the general situation), here we use, as a basic tool, the subordination identity for a model homogeneous system. We also prove a uniqueness result based on the reduction to an operator-differential equation. 相似文献
3.
V. I. Antipin 《Siberian Mathematical Journal》2013,54(2):185-195
We study boundary value problems for operator-differential equations of mixed type, prove existence of generalized solutions, and establish their smoothness in weighted Sobolev spaces. The results are applied to odd order forward-backward equations. 相似文献
4.
We consider the Cauchy problem for a first-order operator-differential equation with singular data. The results are used to study boundary value problems for parabolic equations with operator-valued coefficients. 相似文献
5.
M. K. Balaev 《Mathematical Notes》2011,90(5-6):651-665
We study the Cauchy problem for linear operator-differential equations with unbounded, nondensely defined, variable operator coefficients in a Banach space. We single out new classes of evolution equations of first and second order for which the Cauchy problem is solvable. 相似文献
6.
We consider the problem of minimax control for objects describable by nonlinear operator-differential equations in Banach spaces with restrictions on the phase variables and controls. We prove solvability theorems. The method of proof is based on the theory of extremal problems for generalized operator-differential equations.Translated fromVychislitel'naya i Prikladnaya Matematika, Issue 71, 1990, pp. 114–119. 相似文献
7.
P. V. Vinogradova A. G. Zarubin 《Computational Mathematics and Mathematical Physics》2009,49(9):1567-1575
A projection method is studied as applied to the Cauchy problem for an operator-differential equation with a non-self-adjoint
operator. The operator is assumed to be sufficiently smooth. The linear spans of eigenelements of a self-adjoint operator
are used as projection subspaces. New asymptotic estimates for the convergence rate of approximate solutions and their derivatives
are obtained. The method is applied to initial-boundary value problems for parabolic equations. 相似文献
8.
G. D. Orudzhev 《Ukrainian Mathematical Journal》1994,46(7):1045-1048
We study the Cauchy problem for higher-order operator-differential equations in a Banach space and construct polynomial approximations of its solutions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 952–955, July, 1994. 相似文献
9.
R. Z. Gumbataliev 《Differential Equations》2009,45(10):1451-1459
We study the existence and uniqueness of generalized solutions of a class of boundary value problems for higher-order operator-differential
equations for the case in which the leading part has a multiple characteristic. 相似文献
10.
In this paper, we are concerned with Cauchy problems of fractional differential equations with Riemann–Liouville fractional derivatives in infinite-dimensional Banach spaces. We introduce the notion of fractional resolvent, obtain some its properties, and present a generation theorem for exponentially bounded fractional resolvents. Moreover, we prove that a homogeneous α-order Cauchy problem is well posed if and only if its coefficient operator is the generator of an α-order fractional resolvent, and we give sufficient conditions to guarantee the existence and uniqueness of weak solutions and strong solutions of an inhomogeneous α-order Cauchy problem. 相似文献
11.
We prove the well-posed solvability (in the strong sense) of complete second-order hyperbolic operator-differential equations
with variable domains of unbounded operator coefficients under nonlocal initial conditions. We are the first to establish
the well-posed solvability of the mixed problem for the complete string vibration equation with nonstationary boundary conditions
and nonlocal initial conditions. 相似文献
12.
I. S. Lomov 《Differential Equations》2012,48(5):730-736
We consider problems with point initial data for first-order partial differential equations in a half-strip. The equations contain degeneration with respect to one of the variables. We prove the existence and uniqueness of smooth solutions bounded in a neighborhood of the degeneration. The structure of the considered solutions is established. Such problems arise when solving the Cauchy problem for a system of ordinary differential equations with a movable regular singular point. 相似文献
13.
We prove the existence and uniqueness of global strong solutions to the Cauchy problem of the three-dimensional magnetohydrodynamic equations in R3 when initial data are helically symmetric. Moreover, the large-time behavior of the strong solutions is obtained simultaneously. 相似文献
14.
K. B. Liaskos I. G. Stratis A. N. Yannacopoulos 《Mathematical Methods in the Applied Sciences》2009,32(8):963-985
In this work we present some results on the Cauchy problem for a general class of linear pseudoparabolic equations with additive noise. We consider questions of existence and uniqueness of mild and strong solutions and well posedness for this problem. We also prove the existence and uniqueness of mild and strong solutions for a related perturbed Cauchy problem and we investigate the continuity of the solution with respect to a small parameter. The abstract results are illustrated using examples from electromagnetics and heat conduction. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
15.
Zhong Tan 《Journal of Mathematical Analysis and Applications》2010,364(2):424-436
In this paper we are concerned with the differential system proposed by Shliomis to describe the motion of an incompressible ferrofluid submitted to an external magnetic field. The system consists of the Navier-Stokes equations, the magnetization equations and the magnetostatic equations. No regularizing term is added to the magnetization equations. We prove the local existence of unique strong solution for the Cauchy problem and establish a finite time blow-up criterion of strong solutions. Under the smallness assumption of the initial data and the external magnetic field, we prove the global existence of strong solutions and derive a decay rate of such small solutions in L2-norm. 相似文献
16.
N. A. Aksenov 《Mathematical Notes》2011,90(1-2):175-188
We describe an analog of the Cauchy-Kovalevskaya sufficient conditions for the analytic solvability of the Cauchy problem for systems of operator-differential equations of arbitrary order in locally convex spaces; this analog is stated in terms of the order and type of the linear operator. 相似文献
17.
We prove theorems that characterize the classes of functions whose best approximations by algebraic polynomials tend to zero
with given order. We construct approximations of solutions of operator-differential equations by polynomials in the inverse
operator.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1506–1516, November, 1998. 相似文献
18.
S. E. Zhelezovskii 《Computational Mathematics and Mathematical Physics》2006,46(8):1387-1398
The Cauchy problem for a system of two operator-differential equations is considered that is an abstract statement of linear coupled thermoelasticity problems. Error estimates in the energy norm for the semidiscrete Galerkin method as applied to the Cauchy problem are established without imposing any special conditions on the projection subspaces. By way of illustration, the error estimates are applied to finite element schemes for solving the coupled problem of plate thermoelasticity considered within the framework of the Kirchhoff linearized theory. The results obtained are also applicable to the case when the projection subspaces in the Galerkin method (for the original abstract problem) are the eigenspaces of operators similar to unbounded self-adjoint positive definite operator coefficients of the original equations. 相似文献
19.
We consider Cauchy problems and periodic problems for two-fluid compressible Euler–Maxwell equations arising in the modeling of magnetized plasmas. These equations are symmetrizable hyperbolic in the sense of Friedrichs but don?t satisfy the so-called Kawashima stability condition. For both problems, we prove the global existence and long-time behavior of smooth solutions near a given constant equilibrium state. As a byproduct, we obtain similar results for two-fluid compressible Euler–Poisson equations. 相似文献
20.
Regular solutions to second-order elliptic systems on the plane are representable in terms of A-analytic functions satisfying an operator equation of the Beltrami type. We prove Carleman-type formulas for reconstruction of solutions from data on a part of the boundary of the domain. We use these formulas for solving the Cauchy problems for the system of Lame equations, the Navier–Stokes system, and the system of equations of elasticity with resilience. 相似文献