5 papers
Well-posedness of a first-order formulation for fractionally damped nonlinear acoustics
Pascal Lehner, Mostafa Meliani
In this work, we study the well-posedness of a quasilinear first-order-in-time system with memory arising in nonlinear acoustics. The model features a memory kernel describing the…
A parallel space-time -adaptive discontinuous Galerkin method for nonlinear acoustics
Daniele Corallo, Pascal Lehner, Christian Wieners
In this paper, we introduce and analyze a space-time -adaptive discontinuous Galerkin method for nonlinear acoustics. We first present the underlying mathematical model, which i…
Well-posedness of a first-order-in-time model for nonlinear acoustics with nonhomogeneous boundary conditions
Pascal Lehner
We study well-posedness of a first-order-in-time model for nonlinear acoustics with nonhomogeneous boundary conditions in fractional Sobolev spaces. The analysis proceeds by first…
Infinite dimensional Slow Manifolds for a Linear Fast-Reaction System
Christian Kuehn, Pascal Lehner, Jan-Eric Sulzbach
The aim of this expository paper is twofold. We start with a concise overview of the theory of invariant slow manifolds for fast-slow dynamical systems starting with the work by Ti…
A first order in time wave equation modeling nonlinear acoustics
Barbara Kaltenbacher, Pascal Lehner
In this paper we focus on a small amplitude approximation of a Navier-Stokes-Fourier system modeling nonlinear acoustics. Omitting all third and higher order terms with respect to…