English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We show how the Stefan type free boundary problem with random diffusion inone space dimension can be approximated by the corresponding free boundaryproblem with nonlocal diffusion. The approximation problem is a slightlymodified version of the nonlocal diffusion problem with free boundariesconsidered in [4,8]. The proof relies on the introduction of several auxiliaryfree boundary problems and constructions of delicate upper and lower solutionsfor these problems. As usual, the approximation is achieved by choosing thekernel function in the nonlocal diffusion term of the form $J_\epsilon(x)=\frac1\epsilon J(\frac x\epsilon)$ for small $\epsilon>0$, where $J(x)$ has compactsupport. We also give an estimate of the error term of the approximation bysome positive power of $\epsilon$.

Approximation of random diffusion equation by nonlocal diffusion equation in free boundary problems of one space dimension