Singularly Perturbed C0-semigroups and Nonhomogeneous Differential Equations in Banach Spaces
نویسندگان
چکیده
ABSTRACT. In this paper we study a singular perturbation of an asymptotically convergent operator C0-semigroup, and describe the spectral behaviour and a power series expansion of the perturbed semigroup. As an application of our results we obtain the description of the asymptotic behaviour of the solutions to a nonhomogeneous singularly perturbed differential equation in a Banach space, extending the matrix results of S. Campbell and previous results of the present authors.
منابع مشابه
C0-semigroups of linear operators on some ultrametric Banach spaces
C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric) free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss...
متن کاملNumerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type
In this paper, we have proposed a numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided in...
متن کاملEvolutionary Semigroups and Dichotomy of Linear Skew-product Flows on Locally Compact Spaces with Banach Fibers
We study evolutionary semigroups generated by a strongly continuous semi-cocycle over a locally compact metric space acting on Banach fibers. This setting simultaneously covers evolutionary semigroups arising from nonautonomuous abstract Cauchy problems and C0-semigroups, and linear skew-product flows. The spectral mapping theorem for these semigroups is proved. The hyperbolicity of the semigro...
متن کاملA Parameter Uniform Numerical Scheme for Singularly Perturbed Differential-difference Equations with Mixed Shifts
In this paper, we consider a second-order singularly perturbed differential-difference equations with mixed delay and advance parameters. At first, we approximate the model problem by an upwind finite difference scheme on a Shishkin mesh. We know that the upwind scheme is stable and its solution is oscillation free, but it gives lower order of accuracy. So, to increase the convergence, we propo...
متن کاملA method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers
In this paper, an effective procedure based on coordinate stretching and radial basis functions (RBFs) collocation method is applied to solve singularly perturbed differential-difference equations with layer behavior. It is well known that if the boundary layer is very small, for good resolution of the numerical solution at least one of the collocation points must lie in the boundary layer. In ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006