Approximate controllability of semilinear neutral systems in Hilbert spaces.
Approximate inertial manifolds for nonlinear parabolic equations via steady-state determining mapping.
Approximate methods for calculating the period of oscillations for the generalized Lienard's differential equation
Approximate properties of principal solutions of Volterra-type integrodifferential equations with infinite aftereffect
The integrodifferential system with aftereffect (“heredity” or “prehistory”) dx/dt=Ax+-t R(t,s)x(s,)ds, is considered; here is a positive small parameter, is a constant matrix, is the kernel of this system exponentially decreasing in norm as . It is proved, if matrix and kernel satisfy some restrictions and does not exceed some bound , then the -dimensional set of the so-called principal two-sided solutions approximates in asymptotic sense the infinite-dimensional set of solutions...
Approximate solution of an inhomogeneous abstract differential equation
Recently, we have developed the necessary and sufficient conditions under which a rational function approximates the semigroup of operators generated by an infinitesimal operator . The present paper extends these results to an inhomogeneous equation .
Approximate solution of the nonlinear heat conduction equation in a semi-infinite domain.
Approximate solutions and error bounds for second order operator differential equations
Approximate solutions for integrodifferential equations of the neutral type
The main objective of the present paper is to study the approximate solutions for integrodifferential equations of the neutral type with given initial condition. A variant of a certain fundamental integral inequality with explicit estimate is used to establish the results. The discrete analogues of the main results are also given.
Approximate solutions of abstract differential equations
The methods of arbitrarily high orders of accuracy for the solution of an abstract ordinary differential equation are studied. The right-hand side of the differential equation under investigation contains an unbounded operator which is an infinitesimal generator of a strongly continuous semigroup of operators. Necessary and sufficient conditions are found for a rational function to approximate the given semigroup with high accuracy.
Approximate solutions of matrix differential equations.
A method for solving second order matrix differential equations avoiding the increase of the dimension of the problem is presented. Explicit approximate solutions and an error bound of them in terms of data are given.
Approximate solutions of the forced Duffing equation with mixed nonlinearities.
Approximate trajectories and Lyapunov exponents for dynamical systems
Approximate weak invariance for semilinear differential inclusions in Banach spaces
In this paper we give a criterion for a given set K in Banach space to be approximately weakly invariant with respect to the differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A generates a C 0-semigroup and F is a given multi-function, using the concept of a tangent set to another set. As an application, we establish the relation between approximate solutions to the considered differential inclusion and solutions to the relaxed one, i.e., x′(t) ∈ Ax(t) + F(x(t)), without any Lipschitz conditions...
Approximating the Stability Region for a Differential Equation with a Distributed Delay
We discuss how distributed delays arise in biological models and review the literature on such models. We indicate why it is important to keep the distributions in a model as general as possible. We then demonstrate, through the analysis of a particular example, what kind of information can be gained with only minimal information about the exact distribution of delays. In particular we show that a distribution independent stability region may be obtained in a similar way that delay independent...
Approximation de quelques problèmes de type Stokes par une méthode d'èlements finis mixtes.
Approximation in Lie transformation groups by superposition of one-parameter subgroups. (Approximation in Lieschen Transformationsgruppen durch Überlagerung von einparametrigen Untergruppen.)
Approximation methods for solving the Cauchy problem
In this paper we give some new results concerning solvability of the 1-dimensional differential equation with initial conditions. We study the basic theorem due to Picard. First we prove that the existence and uniqueness result remains true if is a Lipschitz function with respect to the first argument. In the second part we give a contractive method for the proof of Picard theorem. These considerations allow us to develop two new methods for finding an approximation sequence for the solution....
Approximation of analytic functions by Kummer functions.
Approximation of attainable sets of an evolution inclusion of subdifferential type.
Approximation of contact problems with friction