Ausbreitung freier Ränder unter Einfluss von Rauschen: Analysis und Numerik stochastischer degeneriert parabolischer Gleichungen

Drittmittelfinanzierte Einzelförderung


Details zum Projekt

Projektleiter/in:
Prof. Dr. Günther Grün


Beteiligte FAU-Organisationseinheiten:
Professur für Angewandte Mathematik (Analysis und Numerik partieller Differentialgleichungen)

Mittelgeber: Deutsche Forschungsgemeinschaft (DFG)
Mittelgeber: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Projektstart: 01.04.2018
Projektende: 31.03.2020


Abstract (fachliche Beschreibung):

The porous-medium equation and the thin-film equation are prominent
examples of nonnegativity preserving degenerate parabolic equations
which give rise to free boundary problems with the free boundary at time
t > 0 defined as the boundary of the solution’s support at that
time.
As they are supposed to describe the spreading of gas in a
porous-medium or the spreading of a viscous droplet on a horizontal
surface, respectively, mathematical results on the propagation of free
boundaries become relevant in applications. In contrast to, e.g., the
heat equation, where solutions to initial value problems with compactly
supported nonnegative initial data
instantaneously become globally
positive, finite propagation and waiting time phenomena are
characteristic features of degenerate parabolic equations.
In this
project, stochastic partial differential equations shall be studied
which arise from the aforementioned degenerate parabolic equations by
adding multiplicative noise in form of source terms or of convective
terms. The scope is to investigate the impact of noise on the
propagation of free boundaries, including in particular necessary and
sufficient conditions for the occurrence
of waiting time phenomena
and results on the size of waiting times. Technically, the project
relies both on rigorous mathematical analysis and on numerical
simulation.


Zuletzt aktualisiert 2019-29-04 um 14:34