2.1k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Max Planck Institute of Microstructure PhysicsDE112 papers
- Rzeszów University of TechnologyPL27 papers
- Tbilisi State UniversityGE26 papers
- Forschungszentrum JülichDE25 papers
- Centre National de la Recherche ScientifiqueFR24 papers
- Johannes Gutenberg University MainzDE20 papers
- Adam Mickiewicz University in PoznańPL19 papers
- Friedrich Schiller University JenaDE17 papers
- University of KaiserslauternDE17 papers
- Lanzhou UniversityCN16 papers
- Polish Academy of SciencesPL16 papers
- Central South UniversityCN15 papers
32 papers · 1 filter
Nematic liquid crystals: Ericksen-Leslie theory with general stress tensors
Matthias Hieber, Jinkai Li, Mathias Wilke
The Ericksen-Leslie model for nematic liquid crystal flows in case of an isothermal and incompressible fluid with general Leslie stress and anisotropic elasticity, i.e. with genera…
Existence and uniqueness for a coupled parabolic-hyperbolic model of MEMS
Heiko Gimperlein, Runan He, Andrew A. Lacey
Local well-posedness for a nonlinear parabolic-hyperbolic coupled system modelling Micro-Electro-Mechanical System (MEMS) is studied. The particular device considered is a simple c…
Wellposedness of a nonlinear parabolic-dispersive coupled system modelling MEMS
Heiko Gimperlein, Runan He, Andrew A. Lacey
In this paper we study the local wellposedness of the solution to a non-linear parabolic-dispersive coupled system which models a Micro-Electro-Mechanical System (MEMS). A simple e…
Global -estimate for general quasilinear elliptic equations in arbitrary domains of
Siegfried Carl, Hossein Tehrani
In this paper our main goal is to present a new global -estimate for a general class of quasilinear elliptic equations of the form $$ -div \mathcal{A}(x,u,\nabla u)=\math…
Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface
Tomáš Dohnal, Mathias Ionescu-Tira, Marcus Waurick
In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polar…
Quenching for a semi-linear wave equation for MEMS
Heiko Gimperlein, Runan He, Andrew A. Lacey
We consider the formation of finite-time quenching singularities for solutions of semi-linear wave equations with negative power nonlinearities, as can model micro-electro-mechanic…
-calculus for the surface Stokes operator and applications
Gieri Simonett, Mathias Wilke
We consider a smooth, compact and embedded hypersurface without boundary and show that the corresponding (shifted) surface Stokes operator admits a bounded $H^\inft…
A quasilinear transmission problem with application to Maxwell equations with a divergence-free -field
Tomáš Dohnal, Giulio Romani, Daniel P. Tietz
Maxwell equations in the absence of free charges require initial data with a divergence free displacement field . In materials in which the dependence $\mathcal D=\math…
Justification of the Asymptotic Coupled Mode Approximation of Out-of-Plane Gap Solitons in Maxwell Equations
Tomáš Dohnal, Giulio Romani
In periodic media gap solitons with frequencies inside a spectral gap but close to a spectral band can be formally approximated by a slowly varying envelope ansatz. The ansatz is b…
Eigenvalue Bifurcation in Doubly Nonlinear Problems with an Application to Surface Plasmon Polaritons
Tomáš Dohnal, Giulio Romani
We consider a class of generally non-self-adjoint eigenvalue problems which are nonlinear in the solution as well as in the eigenvalue parameter ("doubly" nonlinear). We prove a bi…
Differences between fundamental solutions of general higher order elliptic operators and of products of second order operators
Hans-Christoph Grunau, Giulio Romani, Guido Sweers
We study fundamental solutions of elliptic operators of order with constant coefficients in large dimensions , where their singularities become unbounded. For co…
A maximal regularity approach to the study of motion of a rigid body with a fluid-filled cavity
Giusy Mazzone, Jan Pruess, Gieri Simonett
We consider the inertial motion of a rigid body with an interior cavity that is completely filled with a viscous incompressible fluid. The equilibria of the system are characterize…
On the microscopic bidomain problem with FitzHugh-Nagumo ionic transport
Jan Pruess, Gieri Simonett
The microscopic bidomain problem with FitzHhugh-Nagumo ionic transport is studied in the -framework. Reformulating the problem as a semilinear evolution equation on th…
The Rayleigh-Taylor instability for the Verigin problem with and without phase transition
Jan Pruess, Gieri Simonett, Mathias Wilke
Isothermal compressible two-phase flows in a capillary are modeled with and without phase transition in the presence of gravity, employing Darcy's law for the velocity field. It is…
Uniform bounds for higher-order semilinear problems in conformal dimension
Gabriele Mancini, Giulio Romani
We establish uniform a-priori estimates for solutions of the semilinear Dirichlet problem \begin{equation} \begin{cases} (-Δ)^m u=h(x,u)\quad&\mbox{in }Ω,\\ u=\partial_nu=\cdots=\p…
Critical spaces for quasilinear parabolic evolution equations and applications
Jan Pruess, Gieri Simonett, Mathias Wilke
We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal -regularity in time-wei…
On critical spaces for the Navier-Stokes equations
Jan Pruess, Mathias Wilke
The abstract theory of critical spaces developed in [22] and [20] is applied to the Navier-Stokes equations in bounded domains with Navier boundary conditions as well as no-slip co…
A general existence result for isothermal two-phase flows with phase transition
Maren Hantke, Ferdinand Thein
Liquid-vapor flows with phase transitions have a wide range of applications. Isothermal two-phase flows described by a single set of isothermal Euler equations, where the mass tran…
The Verigin problem with and without phase transition
Jan Pruess, Gieri Simonett
Isothermal compressible two-phase flows with and without phase transition are modeled, employing Darcy's and/or Forchheimer's law for the velocity field. It is shown that the resul…
Optimal regularity and long-time behavior of solutions for the Westervelt equation
Stefan Meyer, Mathias Wilke
We investigate an initial-boundary value problem for the quasilinear Westervelt equation which models the propagation of sound in fluidic media. We prove that, if the initial data…
On the regularity of the interface of a thermodynamically consistent two-phase Stefan problem with surface tension
Jan Pruess, Yuanzhen Shao, Gieri Simonett
We study the regularity of the free boundary arising in a thermodynamically consistent two-phase Stefan problem with surface tension by means of a family of parameter-dependent dif…
Strong solutions in the dynamical theory of compressible fluid mixtures
Matthias Kotschote, Rico Zacher
In this paper we investigate the compressible Navier-Stokes-Cahn-Hilliard equations (the so-called NSCH model) derived by Lowengrub and Truskinowsky. This model describes the flow…
Nonlinear elliptic problems with dynamical boundary conditions of reactive and reactive-diffusive type
Ciprian G. Gal, Martin Meyries
We investigate classical solutions of nonlinear elliptic equations with two classes of dynamical boundary conditions, of reactive and reactive-diffusive type. In the latter case it…
On well-posedness of incompressible two-phase flows with phase transitions: the case of equal densities
Jan Pruess, Senjo Shimizu, Yoshihiro Shibata +1
The basic model for incompressible two-phase flows with phase transitions is derived from basic principles and shown to be thermodynamically consistent in the sense that the total…