97 citations · 112 across the 9 of their papers we have counts for
7 papers · 1 filter
Admissibility criteria for convex integration fan solutions and contact discontinuities in the Euler equation
Heiko Gimperlein
For piecewise constant fan subsolutions to the isentropic Euler equations, the entropy and action rates of any associated convex integration solution, relative to a common referenc…
Analysis of a Model for Electrical Discharge in MEMS
Heiko Gimperlein, Runan He, Andrew A. Lacey
We study the local well-posedness of the solution to a coupled nonlinear elliptic-parabolic system which models electrical discharge in a Micro-Electro-Mechanical System (MEMS). A…
On action rate admissibility criteria
Heiko Gimperlein, Michael Grinfeld, Robin J. Knops +1
We formulate new admissibility criteria for initial value problems motivated by the least action principle. These are applied to a two-dimensional Riemann initial value problem for…
On singular behaviour in a plane linear elastostatics problem
Heiko Gimperlein, Michael Grinfeld, Robin J. Knops +1
A vector field similar to those separately introduced by Artstein and Dafermos is constructed from the tangent to a monotone increasing one-parameter family of non-concentric circl…
The Least Action Admissibility Principle
Heiko Gimperlein, Michael Grinfeld, Robin J. Knops +1
This paper provides a new admissibility criterion for choosing physically relevant weak solutions of the equations of Lagrangian and continuum mechanics when non-uniqueness of solu…
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…