R. Smith

will speak on

Convergence Analysis of the Geometric Thin-Film Equation

Time: 3:00PM
Date: Tue 6th December 2022
Location: Seminar Room SCN 1.25 [map]

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Abstract: The Geometric Thin-Film equation is a mathematical model of droplet spreading in the long-wave limit, which includes a regularization of the contact-line singularity. First, we show that, given initial positive Radon data $\mu \in \mathcal{M}(\R)$, the model admits a weak solution that is $\frac{1}{2}$-H\'older continuous for all time $t \in \R^+$. This solution is based on the push-forward of a function $c:\R^+ \times \R \to \R$ that satisfies a system of ODEs. The function $c$ is shown to be the limit of a sequence of `particle solutions', which take as their initial data finite weighted sums of Dirac measures that approximate $\mu$. Establishing the convergence is non-trivial because the ODE system's interaction kernel possesses singularities. Second, we show that, when restricted to this class of solutions induced in this way, the solution is unique.

\medskip\noindent This is joint work with Lennon \'O N\'araigh and Khang Ee Pang (UCD).

https://ucd-ie.zoom.us/j/65636606500

(This talk is part of the Analysis series.)

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