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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study a class of perturbations for the semilinear wave equation with critical power nonlinearity (in the conformal transform sense). Working in the framework of similarity variables, we introduce a Lyapunov functional for this problem. Using a two-step argument based on interpolation and a critical Gagliardo–Nirenberg inequality, we establish that the blow-up rate of any singular solution is given by the solution of the nonperturbed associated ODE, specifically u″ = up.

LYAPUNOV FUNCTIONAL AND BLOW-UP RESULTS FOR A CLASS OF PERTURBATIONS OF SEMILINEAR WAVE EQUATIONS IN THE CRITICAL CASE