A solution decomposition for a singularly perturbed fourth-order problem

Höhne, Katharina and Franz, Sebastian and Waurick, Marcus (2017) A solution decomposition for a singularly perturbed fourth-order problem. Analysis, 37 (2). pp. 77-100. ISSN 2196-6153

[img]
Preview
Text (Franz-etal-Analysis-2017-A-solution-decomposition-for-a-singularly-perturbed)
Franz_etal_Analysis_2017_A_solution_decomposition_for_a_singularly_perturbed.pdf
Accepted Author Manuscript

Download (254kB)| Preview

    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. To our knowledge, this paper is a first attempt for a solution decomposition of such problems.