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 obtain new $L^1$ contraction results for bounded entropy solutions ofCauchy problems for degenerate parabolic equations. The equations we considerhave possibly strongly degenerate local or non-local diffusion terms. Asopposed to previous results, our results apply without any integrabilityassumption on the %(the positive part of the difference of) solutions. Theytake the form of partial Duhamel formulas and can be seen as quantitativeextensions of finite speed of propagation local $L^1$ contraction results forscalar conservation laws. A key ingredient in the proofs is a new andnon-trivial construction of a subsolution of a fully non-linear (dual)equation. Consequences of our results are maximum and comparison principles,new a priori estimates, and in the non-local case, new existence and uniquenessresults.

$L^1$ contraction for bounded (non-integrable) solutions of degenerate parabolic equations