34 citations · 112 across the 26 of their papers we have counts for
12 papers · 1 filter
A trace theorem for spherical kinetic Sobolev spaces on -convex domains
Herbert Egger, Matthias Schlottbom
Trace theorems are an indispensable tool for the analysis of kinetic equations. They have been established in wide generality by Cessenat and co-workers for radiative transfer and…
Kreiss stability analysis of Hagstrom-Warburton nonreflecting boundary conditions for the first-order time-dependent Maxwell equations
Kaifang Liu, Matthias Schlottbom, J. J. W. van der Vegt +1
We analyze the stability of the Hagstrom-Warburton nonreflecting boundary conditions (HW-NRBCs) for the first-order time-dependent Maxwell equations. The HW-NRBCs enjoy very small…
A kinetic chemotaxis model and its diffusion limit in slab geometry
Herbert Egger, Kathrin Hellmuth, Nora Philippi +1
Chemotaxis describes the intricate interplay of cellular motion in response to a chemical signal. We here consider the case of slab geometry which models chemotactic motion between…
On the unique solvability of radiative transfer equations with polarization
Vincent Bosboom, Matthias Schlottbom, Felix Schwenninger
We investigate the well-posedness of the radiative transfer equation with polarization and varying refractive index. The well-posedness analysis includes non-homogeneous boundary v…
Parameter identification in a structured population model
Alexander Lorz, Jan-Frederik Pietschmann, Matthias Schlottbom
We study parameter identification problems in a structured population model without mutations. Given measurements of the total population size or critical points of the population,…
On the uniqueness of nonlinear diffusion coefficients in the presence of lower order terms
Herbert Egger, Jan-Frederik Pietschmann, Matthias Schlottbom
We consider the identification of nonlinear diffusion coefficients of the form or in quasi-linear parabolic and elliptic equations. Uniqueness for this inverse prob…
Notes on a PDE System for Biological Network Formation
Jan Haskovec, Peter Markowich, Benoit Perthame +1
We present new analytical and numerical results for the elliptic-parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological…
Identification of nonlinear heat conduction laws
Herbert Egger, Jan-Frederik Pietschmann, Matthias Schlottbom
We consider the identification of nonlinear heat conduction laws in stationary and instationary heat transfer problems. Only a single additional measurement of the temperature on a…
Identification of Chemotaxis Models with Volume Filling
Herbert Egger, Jan-Frederik Pietschmann, Matthias Schlottbom
Chemotaxis refers to the directed movement of cells in response to a chemical signal called chemoattractant. A crucial point in the mathematical modeling of chemotactic processes i…
Diffusion asymptotics for linear transport with low regularity
Herbert Egger, Matthias Schlottbom
We provide an asymptotic analysis of linear transport problems in the diffusion limit under minimal regularity assumptions on the domain, the coefficients, and the data. The weak f…
Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem
Herbert Egger, Jan-Frederik Pietschmann, Matthias Schlottbom
In this work we consider the identifiability of two coefficients and in a quasilinear elliptic partial differential equation from observation of the Dirichlet-to-Neum…
An theory for stationary radiative transfer
Herbert Egger, Matthias Schlottbom
We present a self-contained analysis of the stationary radiative transfer equation in weighted spaces. The use of weighted spaces allows us to derive uniform a-priori estimat…