Skeleton decomposition of linear operators in the theory of degenerate differential equations

TL;DR

This paper introduces a skeleton decomposition method for linear operators to transform ill-posed degenerate differential equations into well-posed initial-value problems with unique solutions.

Contribution

The paper proposes a novel skeleton decomposition technique to address ill-posed degenerate differential equations, enabling their reduction to problems with unique solutions.

Findings

Effective reduction of ill-posed equations to well-posed problems

Guarantees of unique solutions for transformed problems

Applicability to a class of degenerate differential equations

Abstract

We suggest method based on the skeleton decomposition of linear operators in order to reduce ill-posed degenerate differential equations to the non-classic initial-value problem enjoying unique solution