30 research outputs found
Local Well-Posedness for Relaxational Fluid Vesicle Dynamics
We prove the local well-posedness of a basic model for relaxational fluid
vesicle dynamics by a contraction mapping argument. Our approach is based on
the maximal -regularity of the model's linearization.Comment: 29 page
Strong Well-Posedness for a Class of Dynamic Outflow Boundary Conditions for Incompressible Newtonian Flows
Based on energy considerations, we derive a class of dynamic outflow boundary
conditions for the incompressible Navier-Stokes equations, containing the
well-known convective boundary condition but incorporating also the stress at
the outlet. As a key building block for the analysis of such problems, we
consider the Stokes equations with such dynamic outflow boundary conditions in
a halfspace and prove the existence of a strong solution in the appropriate
Sobolev-Slobodeckij-setting with (in time and space) as the base space
for the momentum balance. For non-vanishing stress contribution in the boundary
condition, the problem is actually shown to have -maximal regularity under
the natural compatibility conditions. Aiming at an existence theory for
problems in weakly singular domains, where different boundary conditions apply
on different parts of the boundary such that these surfaces meet orthogonally,
we also consider the prototype domain of a wedge with opening angle
and different combinations of boundary conditions: Navier-Slip
with Dirichlet and Navier-Slip with the dynamic outflow boundary condition.
Again, maximal regularity of the problem is obtained in the appropriate
functional analytic setting and with the natural compatibility conditions.Comment: 31 pages, 1 figur
A Kinematic Evolution Equation for the Dynamic Contact Angle and some Consequences
We investigate the moving contact line problem for two-phase incompressible
flows with a kinematic approach. The key idea is to derive an evolution
equation for the contact angle in terms of the transporting velocity field. It
turns out that the resulting equation has a simple structure and expresses the
time derivative of the contact angle in terms of the velocity gradient at the
solid wall. Together with the additionally imposed boundary conditions for the
velocity, it yields a more specific form of the contact angle evolution. Thus,
the kinematic evolution equation is a tool to analyze the evolution of the
contact angle. Since the transporting velocity field is required only on the
moving interface, the kinematic evolution equation also applies when the
interface moves with its own velocity independent of the fluid velocity. We
apply the developed tool to a class of moving contact line models which employ
the Navier slip boundary condition. We derive an explicit form of the contact
angle evolution for sufficiently regular solutions, showing that such solutions
are unphysical. Within the simplest model, this rigorously shows that the
contact angle can only relax to equilibrium if some kind of singularity is
present at the contact line. Moreover, we analyze more general models including
surface tension gradients at the contact line, slip at the fluid-fluid
interface and mass transfer across the fluid-fluid interface.Comment: 25 pages, 6 figures; accepted manuscript
On a Class of Energy Preserving Boundary Conditions for Incompressible Newtonian Flows
We derive a class of energy preserving boundary conditions for incompressible
Newtonian flows and prove local-in-time well-posedness of the resulting initial
boundary value problems, i.e. the Navier-Stokes equations complemented by one
of the derived boundary conditions, in an Lp-setting in domains, which are
either bounded or unbounded with almost flat, sufficiently smooth boundary. The
results are based on maximal regularity properties of the underlying
linearisations, which are also established in the above setting.Comment: 53 page
Stability Analysis for a Class of Heterogeneous Catalysis Models
We prove stability for a class of heterogeneous catalysis models in the
-setting. We consider a setting in a finite three-dimensional pore of
cylinder-like geometry, with the lateral walls acting as a catalytic surface.
Under a reasonable condition on the involved parameters, we show that given
equilibria are normally stable, i.e. solutions are attracted at an exponential
rate. The potential incidence of instability is discussed as well.Comment: 14 page
Global Strong Solutions for a Class of Heterogeneous Catalysis Models
We consider a mathematical model for heterogeneous catalysis in a finite
three-dimensional pore of cylinder-like geometry, with the lateral walls acting
as a catalytic surface. The system under consideration consists of a
diffusion-advection system inside the bulk phase and a
reaction-diffusion-sorption system modeling the processes on the catalytic wall
and the exchange between bulk and surface. We assume Fickian diffusion with
constant coefficients, sorption kinetics with linear growth bound and a network
of chemical reactions which possesses a certain triangular structure. Our main
result gives sufficient conditions for the existence of a unique global strong
-solution to this model, thereby extending by now classical results on
reaction-diffusion systems to the more complicated case of heterogeneous
catalysis.Comment: 30 page
Dihydropyrimidine Dehydrogenase Testing prior to Treatment with 5-Fluorouracil, Capecitabine, and Tegafur: A Consensus Paper
Background: 5-Fluorouracil (FU) is one of the most commonly used cytostatic drugs in the systemic treatment of
cancer. Treatment with FU may cause severe or life-threatening side effects and the treatment-related mortality rate is 0.2–1.0%. Summary: Among other risk factors associated
with increased toxicity, a genetic deficiency in dihydropyrimidine dehydrogenase (DPD), an enzyme responsible for
the metabolism of FU, is well known. This is due to variants
in the DPD gene (DPYD). Up to 9% of European patients carry a DPD gene variant that decreases enzyme activity, and
DPD is completely lacking in approximately 0.5% of patients.
Here we describe the clinical and genetic background and
summarize recommendations for the genetic testing and
tailoring of treatment with 5-FU derivatives. The statement
was developed as a consensus statement organized by the
German Society for Hematology and Medical Oncology in
cooperation with 13 medical associations from Austria, Germany, and Switzerland. Key Messages: (i) Patients should be
tested for the 4 most common genetic DPYD variants before
treatment with drugs containing FU. (ii) Testing forms the
basis for a differentiated, risk-adapted algorithm with recommendations for treatment with FU-containing drugs. (iii)
Testing may optionally be supplemented by therapeutic
drug monitorin