A Singular 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

inhomogeneous two-parameter abstract cauchy problem

Nonuniqueness Theorem for a Singular Cauchy-nicoletti Problem

The nonuniqueness of a regular or singular Cauchy problem for ordinary differential equations is studied in several papers such as [3, 4, 5, 13, 14, 15, 16, 17]. Most of these results can also be found in the monograph [1]. The uniqueness of solutions of Cauchy initial value problem for ordinary differential equations with singularity is investigated in [7, 8, 9, 12]. The topological structure ...

A Numerical Method for Cauchy Problem Using Singular Value Decomposition

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of the domain, ...