7 papers · 1 filter
A semiconvex counterexample to energy monotonicity for time-fractional gradient flows
Marvin Fritz
For time-fractional gradient flows, natural dissipation statements are often integrated or memory-modified rather than pointwise differential inequalities for the original energy.…
On the well-posedness of a nonlocal kinetic model for dilute polymers with anomalous diffusion
Marvin Fritz, Endre Süli, Barbara Wohlmuth
In this work, we study a class of nonlocal-in-time kinetic models of incompressible dilute polymeric fluids. The system couples a macroscopic balance of linear momentum equation wi…
Well-posedness and simulation of weak solutions to the time-fractional Fokker-Planck equation with general forcing
Marvin Fritz
In this paper, we investigate the well-posedness of weak solutions to the time-fractional Fokker-Planck equation. Its dynamics is governed by anomalous diffusion, and we consider t…
Analysis of a dilute polymer model with a time-fractional derivative
Marvin Fritz, Endre Süli, Barbara Wohlmuth
We investigate the well-posedness of a coupled Navier-Stokes-Fokker-Planck system with a time-fractional derivative. Such systems arise in the kinetic theory of dilute solutions of…
Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation
Marvin Fritz, Ernesto A. B. F. Lima, Vanja Nikolić +2
We present and analyze new multi-species phase-field mathematical models of tumor growth and ECM invasion. The local and nonlocal mathematical models describe the evolution of volu…
On the unsteady Darcy-Forchheimer-Brinkman equation in local and nonlocal tumor growth models
Marvin Fritz, Ernesto A. B. F. Lima, J. Tinsley Oden +1
A mathematical analysis of local and nonlocal phase-field models of tumor growth is presented that includes time-dependent Darcy-Forchheimer-Brinkman models of convective velocity…