54 citations · 299 across the 38 of their papers we have counts for
14 papers · 1 filter
Theory of shifts, shocks, and the intimate connections to -type a posteriori error analysis of numerical schemes for hyperbolic problems
Jan Giesselmann, Sam G. Krupa
In this paper, we develop reliable a posteriori error estimates for numerical approximations of scalar hyperbolic conservation laws in one space dimension. Our methods have no inhe…
Regularity and long time behavior of a doubly nonlinear parabolic problem and its discretization
Herbert Egger, Jan Giesselmann
We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds…
An Observer for pipeline flow with hydrogen blending in gas networks: exponential synchronization
Martin Gugat, Jan Giesselmann
We consider a state estimation problem for gas flows in pipeline networks where hydrogen is blended into the natural gas. The flow is modeled by the quasi-linear isothermal Euler e…
Observer-based data assimilation for barotropic gas transport using distributed measurements
Jan Giesselmann, Martin Gugat, Teresa Kunkel
We consider a state estimation problem for gas pipeline flow modeled by the one-dimensional barotropic Euler equations. In order to reconstruct the system state, we construct an ob…
On a nodal observer for a semilinear model for the flow in gas networks
Martin Gugat, Jan Giesselmann, Teresa Kunkel
The flow of gas through networks of pipes can be modeled by coupling hyperbolic systems of partial differential equations that describe the flow through the pipes that form the edg…
Stability and asymptotic analysis for instationary gas transport via relative energy estimates
Herbert Egger, Jan Giesselmann
We consider the transport of gas in long pipes and pipeline networks for which the dynamics are dominated by friction at the pipe walls. The governing equations can be formulated a…
Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model
Jan Giesselmann, Niklas Kolbe, Maria Lukacova-Medvidova +1
We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families, migrate on the extracellular matrix and proliferate. Moreover the model de…
Stability properties of the Euler-Korteweg system with nonmonotone pressures
Jan Giesselmann, Athanasios E. Tzavaras
We establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hill…
Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary
Jan Giesselmann, Philippe G. LeFloch
We study nonlinear hyperbolic conservation laws posed on a differential (n+1)-manifold with boundary referred to as a spacetime, and defined from a prescribed flux field of n-forms…
Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics
Jan Giesselmann, Corrado Lattanzio, Athanasios E. Tzavaras
For an Euler system, with dynamics generated by a potential energy functional, we propose a functional format for the relative energy and derive a relative energy identity. The lat…
The problem of dynamic cavitation in nonlinear elasticity
Jan Giesselmann, Alexey Miroshnikov, Athanasios E. Tzavaras
The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example…
Modeling of compressible electrolytes with phase transition
Wolfgang Dreyer, Jan Giesselmann, Christiane Kraus
A novel thermodynamically consistent diffuse interface model is derived for compressible electrolytes with phase transitions. The fluid mixtures may consist of N constituents with…
Relative entropy in multi-phase models of 1d elastodynamics: Convergence of a non-local to a local model
Jan Giesselmann
In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model conv…
Singular limiting induced from continuum solutions and the problem of dynamic cavitation
Jan Giesselmann, Athanasios E. Tzavaras
In the works of K.A. Pericak-Spector and S. Spector \cite{ps88, ps98} a class of self-similar solutions are constructed for the equations of radial isotropic elastodynamics that de…