Open AccessGlobal existence and blow-up results for a nonlinear model for a dynamic suspension bridge
Author(s) -
Quang-Minh Tran,
Hong-Danh Pham
Publication year - 2021
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021135
Subject(s) - term (time) , upper and lower bounds , nonlinear system , suspension (topology) , mathematics , space (punctuation) , mathematical analysis , variable coefficient , order (exchange) , control theory (sociology) , physics , computer science , pure mathematics , economics , control (management) , quantum mechanics , artificial intelligence , homotopy , operating system , finance
The paper deals with global existence and blow-up results for a class of fourth-order wave equations with nonlinear damping term and superlinear source term with the coefficient depends on space and time variable. In the case the weak solution is global, we give information on the decay rate of the solution. In the case the weak solution blows up in finite time, estimate the lower bound and upper bound of the lifespan of the blow-up solution, and also estimate the blow-up rate. Finally, if our problem contains an external vertical load term, a sufficient condition is also established to obtain the global existence and general decay rate of weak solutions.