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math.AP2022★ 1 cited
Green's function estimates for a 2d singularly perturbed convection-diffusion problem: extended analysis
Sebastian Franz, Natalia Kopteva
This paper presents an extended version of the article [Franz, S., Kopteva, N.: J. Differential Equations, 252 (2012)]. The main improvement compared to the latter is in that here…
math.AP2017
Resolvent estimates and numerical implementation for the homogenisation of one-dimensional periodic mixed type problems
Sebastian Franz, Marcus Waurick
We study a homogenisation problem for problems of mixed type in the framework of evolutionary equations. The change of type is highly oscillatory. The numerical treatment is done b…
math.AP2015
A solution decomposition for a singularly perturbed fourth-order problem
Sebastian Franz, Katharina Höhne, Marcus Waurick
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…