Application of Rothe's method to abstract parabolic equations
Application of Rothe's method to nonlinear evolution equations
Application of Rothe's method to parabolic variational inequalities
Application of Rothe's method to perturbed linear hyperbolic equations and variational inequalities
Application of the Mean Ergodic Theorem to Certain Semigroups
Applications of the Carathéodory theorem to PDEs
We discuss and exploit the Carathéodory theorem on existence and uniqueness of an absolutely continuous solution x: ℐ (⊂ ℝ) → X of a general ODE for the right-hand side ℱ : dom ℱ ( ⊂ ℝ × X) → X taking values in an arbitrary Banach space X, and a related result concerning an extension of x. We propose a definition of solvability of (*) admitting all connected ℐ and unifying the cases “dom ℱ is open” and “dom ℱ = ℐ × Ω for some Ω ⊂ X”. We show how to use the theorems mentioned above to get approximate...
Approximate inertial manifolds for nonlinear parabolic equations via steady-state determining mapping.
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 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 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...
Approximation of attainable sets of an evolution inclusion of subdifferential type.
Approximation of Hopf Bifurcation.
Approximation of solutions to evolution integrodifferential equations.
Approximation theorem for evolution operators
This paper is devoted to the study of the approximation problem for the abstract hyperbolic differential equation u'(t) = A(t)u(t) for t ∈ [0,T], where A(t):t ∈ [0,T] is a family of closed linear operators, without assuming the density of their domains.
Approximation von Eigenwertproblemen bei nichtlinearer Parameterabhängigkeit.
Approximations and error bounds for computing the inverse mapping
In this paper we propose a procedure to construct approximations of the inverse of a class of differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.
Approximations of solutions to nonlinear Sobolev type evolution equations.
Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients
In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.