共查询到20条相似文献,搜索用时 31 毫秒
1.
M. Otelbaev A. A. Durmagambetov Ye. N. Seitkulov 《Proceedings of the Steklov Institute of Mathematics》2008,260(1):194-203
We study a nonlinear operator differential equation in a Hilbert space. This equation represents an abstract model for the system of Navier-Stokes equations. The main result consists in proving the existence of a strong solution to this equation under the condition that a certain other system of equations (related to the original equation) has only the zero solution. 相似文献
2.
Chun-Hua Guo 《Numerical Functional Analysis & Optimization》2013,34(5):516-529
We start with a discussion of coupled algebraic Riccati equations arising in the study of linear-quadratic optimal control problems for Markov jump linear systems. Under suitable assumptions, this system of equations has a unique positive semidefinite solution, which is the solution of practical interest. The coupled equations can be rewritten as a single linearly perturbed matrix Riccati equation with special structures. We study the linearly perturbed Riccati equation in a more general setting and obtain a class of iterative methods from different splittings of a positive operator involved in the Riccati equation. We prove some special properties of the sequences generated by these methods and determine and compare the convergence rates of these methods. Our results are then applied to the coupled Riccati equations of jump linear systems. We obtain linear convergence of the Lyapunov iteration and the modified Lyapunov iteration, and confirm that the modified Lyapunov iteration indeed has faster convergence than the original Lyapunov iteration. 相似文献
3.
Thomas P. Witelski 《Studies in Applied Mathematics》1996,97(3):277-300
We study the structure of diffusive layers in solutions of unstable nonlinear diffusion equations. These equations are regularizations of the forward-backward heat equation and have diffusion coefficients that become negative. Such models include the Cahn-Hilliard equation and the pseudoparabolic viscous diffusion equation. Using singular perturbation methods we show that the balance between diffusion and higher-order regularization terms uniquely determines the interface structure in these equations. It is shown that the well-known “equal area” rule for the Cahn-Hilliard equation is a special case of a more general rule for shock construction in the viscous Cahn-Hilliard equation. 相似文献
4.
We consider the construction of Dirichlet series for quasilinear partial differential equations. We obtain a remarkable result that for the class of equations under study, the only equations that admit such a series solution are transformable back onto the only known integrable equation within the class. 相似文献
5.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(11):4215-4231
The modified method of simplest equation is powerful tool for obtaining exact and approximate solutions of nonlinear PDEs. These solutions are constructed on the basis of solutions of more simple equations called simplest equations. In this paper we study the role of the simplest equation for the application of the modified method of simplest equation. We follow the idea that each function constructed as polynomial of a solution of a simplest equation is a solution of a class of nonlinear PDEs. We discuss three simplest equations: the equations of Bernoulli and Riccati and the elliptic equation. The applied algorithm is as follows. First a polynomial function is constructed on the basis of a simplest equation. Then we find nonlinear ODEs that have the constructed function as a particular solution. Finally we obtain nonlinear PDEs that by means of the traveling-wave ansatz can be reduced to the above ODEs. By means of this algorithm we make a first step towards identification of the above-mentioned classes of nonlinear PDEs. 相似文献
6.
In this paper we consider two boundary-value problems in a band for higher-order degenerate elliptic equations. These equations degenerate on one boundary of the band to a third-order equation with respect to one variable. We study problems in weight spaces similar to Sobolev ones whose norms are constructed with the help of a certain integral transform. We obtain a priori estimates in these weight spaces for solutions to boundary-value problems in the band for higher-order elliptic equations that degenerate on one boundary of the band to a third-order equation with respect to one variable. 相似文献
7.
V. A. Bel’skii 《Differential Equations》2012,48(1):11-18
We consider a technique for constructing first-order differential equations with polynomial right-hand sides and with Mironenko
reflective function coinciding with that of a given polynomial equation. We study relations between equations constructed
by this technique. 相似文献
8.
A. V. Chernov 《Russian Mathematics (Iz VUZ)》2012,56(3):55-65
We study a nonlinear controlled functional operator equation in an ideal Banach space. We establish sufficient conditions
for the global solvability for all controls from a given set, and obtain a pointwise estimate for solutions. Using upper and
lower estimates of the functional component in the right-hand side of the initial equation (with a fixed operator component),
we obtain majorant and minorant equations. We prove the stated theorem, assuming the monotonicity of the operator component
in the right-hand side and the global solvability of both majorant andminorant equations. We give examples of the reduction
of controlled initial boundary value problems to the equation under consideration. 相似文献
9.
Miguel V.S. Frasson 《Applied mathematics and computation》2009,214(1):66-72
We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. 相似文献
10.
11.
E. Weinan 《纯数学与应用数学通讯》1992,45(3):301-326
We study the homogenization of the linear and nonlinear transport equations with oscillatory velocity fields. Two types of homogenized equations are derived. For general n-dimensional linear and nonlinear problems, we derive homogenized equations by introducing additional independent variables to represent the small scales. For the two-dimensional linear transport equations, we derive effective equations for the averaged quantities. Such equations take the form of either a degenerate non-local diffusion equation with memory or a higher order hyperbolic equation. To study the nonlinear transport equations we introduce the concept of two-scale Young measure and extend DiPerna's method to prove that it reduces to a family of Dirac measures. 相似文献
12.
Shuji Machihara 《Journal of Mathematical Analysis and Applications》2003,281(2):552-564
We study the inviscid limit of the complex Ginzburg-Landau equation. We observe that the solutions for the complex Ginzburg-Landau equation converge to the corresponding solutions for the nonlinear Schrödinger equation. We give its convergence rate. We estimate the integral forms of solutions for two equations. 相似文献
13.
We study a system of two equations of the parabolic type with two nonlinearities depending on the sum of squares of two unknown functions. We derive conditions under which the system can be reduced to a single equation. We indicate conditions under which this equation can be reduced to a linear heat equation or to semilinear equations. We construct parametric families of exact solutions defined by elementary functions. We derive a control law providing the existence of a wide class of functions that can be realized as exact solutions. 相似文献
14.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(8):951-956
We present, for the BGK equation, asymptotic limits leading to various equations of incompressible and compressible fluid mechanics: the Navier-Stokes equations, the linearized Navier-Stokes equations, the Euler equation, the linearized Euler equation, and the compressible Euler equation. We state a convergence theorem for the nonlinear Navier-Stokes, as well as a result for the linear Navier-Stokes case, and for the compressible Euler equation. 相似文献
15.
D. V. Turtin 《Russian Mathematics (Iz VUZ)》2010,54(9):77-79
We study linear partial differential equations with increasing coefficients in a half-plane. We establish maximal nonuniqueness
classes of solutions to the Cauchy problem for these equations. The proof is based on a new estimation method for a solution
to the dual differential equation with a parameter. 相似文献
16.
We consider a multiparameter spectral problem for a weakly coupled system of ordinary differential equations in which every equation is Hamiltonian and contains two unknown functions. Using the notion of the number of an eigenvalue for a problem with one such equation, we give a statement of the problem of finding the desired eigentuple of values for the problem with several equations. We prove the existence and uniqueness of a solution of this problem and suggest and study a numerical solution method. 相似文献
17.
G. G. Poletaev 《Ukrainian Mathematical Journal》1991,43(9):1124-1135
We study an abstract dual equation which is an analogue of a dual integral equation of convolution type in a ring with a factorization pair of subrings. In general, the coefficients of this equation can belong to different equations with factorization pairs. We study the relation between the solvability of equations and the factorablity of certain elements constructed from their coefficients.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 9, pp. 1201–1213, September, 1991. 相似文献
18.
S. A. Salem 《Journal of Applied Mathematics and Computing》2006,21(1-2):331-355
We study a model procedure to solve the incompressible Navier-Stokes equations on the flow inside contraction geometry. The governing equations are expressed in the primitive variable formulation. A rectangular computational plane is arises by elliptic grid generation technique. The numerical solution is based on a technique of automatic numerical generation of a curvilinear coordinate system. By transformed the governing equation into computational plane. The time dependent momentum equations are solved explicitly for the velocity field using the explicit marching procedure, the continuity equation is applied at each grid point in the solution of pressure equation, while the successive over relaxation (SOR) method is used for the Neumann problem for pressure. We will apply the technique on several irregular-shape. 相似文献
19.
We study here an initial-value problem for the Degasperis–Procesi equation with a strong dispersive term, which is an approximation to the incompressible Euler equations for shallow water waves. We first determine the blow-up set of breaking waves to the equation. We then prove the existence and uniqueness of global weak solutions to the equation with certain initial profiles. 相似文献
20.
We study the Hamilton-Jacobi equation for undiscounted exit time
control problems with general nonnegative Lagrangians using the
dynamic programming approach. We prove theorems characterizing the
value function as the unique bounded-from-below viscosity solution
of the Hamilton-Jacobi equation that is null on the target. The
result applies to problems with the property that all trajectories
satisfying a certain integral condition must stay in a bounded
set. We allow problems for which the Lagrangian is not uniformly
bounded below by positive constants, in which the hypotheses of
the known uniqueness results for Hamilton-Jacobi equations are not
satisfied. We apply our theorems to eikonal equations from
geometric optics, shape-from-shading equations from image
processing, and variants of the Fuller Problem. 相似文献