Decay estimates for a plate equation with supercritical damping and a logarithmic source term

Decay estimates for a plate equation with supercritical damping and a logarithmic source term | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 3 February 2026 V1 Latest version Share on Decay estimates for a plate equation with supercritical damping and a logarithmic source term Authors : Xiaolei Li [email protected] , ShuKe Xiao , and Bin Guo 0000-0003-0057-1332 Authors Info & Affiliations https://doi.org/10.22541/au.177011290.08388976/v1 114 views 62 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this paper, a plate equation involving supercritical damping and a logarithmic source term is considered. It is evident that the energy of the solution exhibits exponential decay in the linear case, with polynomial decay occurring in the subcritical case. However, the estimation is complicated in the supercritical cases, due to the failure of the embedding inequality and the presence of the logarithmic source, conventional multiplier approaches are unsuccessful. Motivated by Haraux and Tebou, a priori estimate for the integral ∫ Ω | u | m d x is provided. Subsequently, by combining the Nehari functional estimates and applying a modified multiplier method, we establish the logarithmical decay of the energy. Supplementary Material File (main document - latex pdf.pdf) Download 371.53 KB Information & Authors Information Version history V1 Version 1 03 February 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords logarithmic nonlinearity plate equation supercritical damping Authors Affiliations Xiaolei Li [email protected] Changchun University of Science and Technology View all articles by this author ShuKe Xiao Changchun University of Science and Technology View all articles by this author Bin Guo 0000-0003-0057-1332 Jilin University View all articles by this author Metrics & Citations Metrics Article Usage 114 views 62 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Xiaolei Li, ShuKe Xiao, Bin Guo. Decay estimates for a plate equation with supercritical damping and a logarithmic source term. Authorea . 03 February 2026. DOI: https://doi.org/10.22541/au.177011290.08388976/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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