A solution decomposition for a singularly perturbed fourth-order problem

TL;DR

This paper introduces a solution decomposition technique for a singularly perturbed fourth-order problem with third-order terms, using a formal power series approach to analyze solution structure and existence.

Contribution

It presents a novel decomposition method for singularly perturbed fourth-order problems, addressing solution existence and structure via reduced third-order problems.

Findings

Decomposition into reduced problems and layer parts.

Existence of unique solutions for original and reduced problems.

Formal power series approach effectively analyzes solution structure.

Abstract

We consider a singularly perturbed fourth-order problem with third-order terms on the unit square. With a formal power series approach, we decompose the solution into solutions of reduced (third-order) problems and various layer parts. The existence of unique solutions for the problem itself and for the reduced third-order problems is also addressed.