35 citations · 253 across the 16 of their papers we have counts for
16 papers
A coercive space-time variational approach to fractional diffusion problems
Herbert Egger, Marvin Fritz, Barbara Wohlmuth
We consider a fractional diffusion problem with temporal nonlocality acting on the diffusive flux. A coercive space--time variational formulation in Bochner-valued fractional Sobol…
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…
Tumor evolution models of phase-field type with nonlocal effects and angiogenesis
Marvin Fritz
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary character…
A phase-field model for non-small cell lung cancer under the effects of immunotherapy
Andreas Wagner, Pirmin Schlicke, Marvin Fritz +4
Formulating tumor models that predict growth under therapy is vital for improving patient-specific treatment plans. In this context, we present our recent work on simulating non-sm…
A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue
Marvin Fritz, Tobias Köppl, J. Tinsley Oden +3
In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are conside…
Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy
Marvin Fritz, Ustim Khristenko, Barbara Wohlmuth
Time-fractional partial differential equations are nonlocal in time and show an innate memory effect. In this work, we propose an augmented energy functional which includes the his…
Time-fractional Cahn-Hilliard equation: Well-posedness, degeneracy, and numerical solutions
Marvin Fritz, Mabel L. Rajendran, Barbara Wohlmuth
In this paper, we derive the time-fractional Cahn-Hilliard equation from continuum mixture theory with a modification of Fick's law of diffusion. This model describes the process o…
Modeling and simulation of vascular tumors embedded in evolving capillary networks
Marvin Fritz, Prashant K. Jha, Tobias Köppl +3
In this work, we present a coupled 3D-1D model of solid tumor growth within a dynamically changing vascular network to facilitate realistic simulations of angiogenesis. Additionall…
On a subdiffusive tumour growth model with fractional time derivative
Marvin Fritz, Christina Kuttler, Mabel L. Rajendran +2
In this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of subdiffusion, mechanical effects, nutrien…
Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network
Marvin Fritz, Prashant K. Jha, Tobias Köppl +2
In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The…
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…
Well-posedness and numerical treatment of the Blackstock equation in nonlinear acoustics
Marvin Fritz, Vanja Nikolić, Barbara Wohlmuth
We study the Blackstock equation which models the propagation of nonlinear sound waves through dissipative fluids. Global well-posedness of the model with homogeneous Dirichlet bou…