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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove the property of finite speed of propagation for degenerate parabolic equations of order 2m 2, when the nonlinearity is of general type, and not necessarily a power function. We also give estimates of the growth in time of the interface bounding the support of the solution. In the case of the thin-film equation, with non-power nonlinearity, we obtain sharp results, in the range of nonlinearities we consider. Our optimality result seems to be new even in the case of power nonlinearities with general initial data. In the case of the Cauchy problem for degenerate equations with general m, our main assumption is a suitable integrability Dini condition to be satisfied by the nonlinearity itself. Our results generalize Bernis’ estimates for higher-order equations with power structures. In the case of second-order equations we also prove L∞ estimates of solutions.

Finite speed of propagation for the thin-film equation and other higher-order parabolic equations with general nonlinearity