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Subject of consideration is the analytical investigation of a coupled system of partial differential equations arising from the modelling of electrostatically actuated microelectromechanical systems with general permittivity profile. A quasilinear parabolic evolution problem for the displacement...
be a Dirichlet form on
is locally compact
-compact measure space. Assume
is inner regular, i.e., regular in restriction to functions...
In a recent paper we presented a general perturbation result for generators of
-semigroups, c.f. Theorem 2.1 below. The aim of the present work is to replace, in case the unperturbed semigroup is analytic, the various admissibility conditions appearing in this result by simpler...
In this paper we discuss the stability of geodesic spheres in
under constrained curvature flows. We prove that under some standard assumptions on the speed and weight functions, the spheres are stable under perturbations that preserve a volume type quantity.
We consider a nonlinear integro-differential equation for prion proliferation that includes prion polymerization, polymer splitting, and polymer joining. The equation can be written as a quasilinear Cauchy problem. For bounded reaction rates we prove global existence and uniqueness of classical...
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