Global existence of solutions to semi-linear σ-evolution equations with different damping types in Lq framework

Global existence of solutions to semi-linear σ-evolution equations with different damping types in Lq framework | 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 Search Search ADVANCED SEARCH SCROLL Mathematical Methods in the Applied Sciences This is a preprint and has not been peer reviewed. Data may be preliminary. 30 January 2025 V1 Latest version Share on Global existence of solutions to semi-linear σ-evolution equations with different damping types in Lq framework Authors : Dinh Van Duong , Tuan Anh Dao 0000-0003-4578-4235 [email protected] , and Thi Nga Bui Authors Info & Affiliations https://doi.org/10.22541/au.173827658.83498534/v1 555 views 247 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this paper, we would like to study the Cauchy problem for linear σ -evolution equations with mixing the parabolic like damping term corresponding to σ 1 ∈ [ 0, σ / 2 ) and the σ -evolution like damping corresponding to σ 2 ∈ ( σ / 2, σ ] . The main goals are on the one hand to conclude some estimates for solutions and their derivatives in the L q setting, with any q ∈[1 , ∞], by developing the theory of modified Bessel functions effectively to control Fourier multipliers appearing the solution representation formula in a competition between these two kinds of damping. On the other hand, we are going to prove the global (in time) existence of small data Sobolev solutions in the treatment of the corresponding semi-linear equations by applying ( L m ∩ L q ) - L q and L q - L q estimates, with q ∈(1 , ∞) and m ∈[1 ,q ), from the linear models. Thanks to flexible choices of parameters q,m and even suitably required regularities, one recognizes that not only some restrictions for power exponents can be relaxed, but also they allow us to conclude an existence result for global solutions with arbitrarily small regularity in terms of dealing with the semi-linear equations. Supplementary Material File (mmas_duongdaonga_2025.01.25.pdf) Download 357.97 KB Information & Authors Information Version history V1 Version 1 30 January 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Collection Mathematical Methods in the Applied Sciences Keywords $\sigma$-evolution like damping fourier multipliers global existence parabolic like damping Authors Affiliations Dinh Van Duong Hanoi University of Science and Technology View all articles by this author Tuan Anh Dao 0000-0003-4578-4235 [email protected] Hanoi University of Science and Technology View all articles by this author Thi Nga Bui Hanoi University of Science and Technology View all articles by this author Metrics & Citations Metrics Article Usage 555 views 247 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Dinh Van Duong, Tuan Anh Dao, Thi Nga Bui. Global existence of solutions to semi-linear σ-evolution equations with different damping types in Lq framework. Authorea . 30 January 2025. DOI: https://doi.org/10.22541/au.173827658.83498534/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. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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