Alexander Mielke, Roland R. Netz, Sina Zendehroud
Published 2020-04-24Version 1
We consider a linear system that consists of a linear wave equation on a horizontal hypersurface and a parabolic equation in the half space below. The model describes longitudinal elastic waves in organic monolayers at the water-air interface, which is an experimental setup that is relevant for understanding wave propagation in biological membranes. We study the scaling regime where the relevant horizontal length scale is much larger than the vertical length scale and provide a rigorous limit leading to a fractionally-damped wave equation for the membrane. We provide the associated existence results via linear semigroup theory and show convergence of the solutions in the scaling limit. Moreover, based on the energy-dissipation structure for the full model, we derive a natural energy and a natural dissipation function for the fractionally-damped wave equation with a time derivative of order 3/2
The rigorous derivation of the $\mathbb{T}^{2}$ focusing cubic NLS from 3D
Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation
Theories for incompressible rods: a rigorous derivation via $Γ$-convergence
![QR code for arXiv:2004.11830 [math.AP]](http://oss.arxitics.com/images/favicon.svg)