Entire Solutions of the Abstract Cauchy Problem in a Hilbert Space

Inhomogeneous Two-Parameter Abstract Cauchy Problem

A singular abstract cauchy problem.

In this note a singular abstract Cauchy problem is considered. A solution is obtained for this problem in terms of a regular abstract Cauchy problem. As an application we obtain a new solution of the initial value problem for a class of singular partial differential equations.

inhomogeneous two-parameter abstract cauchy problem

Singularly Perturbed Cauchy Problem for Abstract Linear Differential Equations of Second Order in Hilbert Spaces∗

We study the behavior of solutions to the problem { ε (u′′ ε (t) +A1uε(t)) + u ′ ε(t) +A0uε(t) = fε(t), t ∈ (0, T ), uε(0) = u0ε, uε(0) = u1ε, as ε → 0, where A1 and A0 are two linear self-adjoint operators in a Hilbert space H. MSC: 35B25, 35K15, 35L15, 34G10 keywords: singular perturbations; Cauchy problem; boundary layer function.

Computable Analysis of the Abstract Cauchy Problem in a Banach Space and Its Applications (I)

We study computability of the abstract linear Cauchy problem du(t)/dt = Au(t), u(0) = x ∈ X, (1) where A is a linear operator, possibly unbounded, on a Banach space X. We give necessary and sufficient conditions for A such that the solution operator K : x → u of the problem (1) is computable. For studying computability we use the representation approach to Computable Analysis developed by Weihr...