Stability For Nonlinear Evolution Equations Research Articles

Numerical stability for nonlinear evolution equations

The paper deals with discretisation methods for nonlinear operator equations written as abstract nonlinear evolution equations. Brezis and Pazy showed that the solution of such problems is given by nonlinear semigroups whose theory was founded by Crandall and Liggett. By using the approximation theorem of Brezis and Pazy, we show the N-stability of the abstract nonlinear discrete problem for the implicit Euler method. Motivated by the rational approximation methods for linear semigroups, we propose a more general time discretisation method and prove its N-stability as well.

The Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations

AbstractThe impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations. The sensitivity of the difference scheme to initial values is further analyzed. The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined. Thus, the computational stability is sensitive to the initial perturbations.

Linearized stability for nonlinear evolution equations

Linearized stability for nonlinear evolution equations

A Principle of Linearized Stability for Nonlinear Evolution Equations

We present a principle of linearized stability of stationary solutions to nonlinear evolution equation in Banach spaces. The well-known semilinear case is shown to fit into our framework. Applications to nonlinear population dynamics and to functional differential equations are also considered.

A principle of linearized stability for nonlinear evolution equations

We present a principle of linearized stability of stationary solutions to nonlinear evolution equation in Banach spaces. The well-known semilinear case is shown to fit into our framework. Applications to nonlinear population dynamics and to functional differential equations are also considered.

Existence, uniqueness, and stability of nonlinear evolution equations

In this paper we study existence, uniqueness, and stability of nonlinear evolution equations. We develop a new type of perturbation result for a C 0 semigroup in Banach space, where the nonlinear operators are not necessarily m-accretive or everywhere defined. Assuming that the semigroup has a smoothing property we obtain local existence, uniqueness and regularity results. We then establish a Liapunov theory which enables us to examine stability. To illustrate our theory several simple examples are presented.