Classification of asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients: Effective damping case

Autor:	Yuta Wakasugi, Shuji Yoshikawa
Rok vydání:	2021
Předmět:	010101 applied mathematics Applied Mathematics 010102 general mathematics Mathematical analysis Initial value problem 0101 mathematics 01 natural sciences Scaling Analysis Beam (structure) Variable (mathematics) Mathematics
Zdroj:	Journal of Differential Equations. 272:938-957
ISSN:	0022-0396
Popis:	We consider the Cauchy problem for the linear beam equation with two variable coefficients: u t t + b ( t ) u t + u x x x x − a ( t ) u x x = 0 , ( t , x ) ∈ R + × R . The purpose of this study is to classify the behavior of solution with respect to ( α , β ) when the coefficients a and b behave as a ( t ) ∼ ( 1 + t ) α and b ( t ) ∼ ( 1 + t ) β . In this article we shall give the asymptotic profile formula in effective damping cases, by using the method of scaling variables developed by Gallay and Raugel [9] .
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::9e7d76032e42c87ebe5bf73d749ad7aa https://doi.org/10.1016/j.jde.2020.10.008 Zobrazit plný text záznamu Full Text from ScienceDirect