A solution decomposition for a singularly perturbed fourth-order problem

2015/11/17 by Sebastian Franz, Franz, Sebastian, Katharina Höhne +3
Computer Science · Engineering · Mathematics · #35B25 #35C20 #35G15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Material Science and Thermodynamics

paper · pdf · doi:10.48550/arxiv.1511.05378

openalex publication_date 2015/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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