Global nonexistence of solutions for von Karman equations with variable exponents. (December 2018)

• Record Type: Journal Article
• Authors: Kang, Jum-Ran
• Is Part Of: Applied mathematics letters. Volume 86(2018)
• Page Start: 249
• Page End: 255
• Publication Date: 2018-12
• Subjects: Blow-up -- Von Karman equations -- Variable exponents; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2018.07.008
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We consider the von Karman equations with variable exponents: u t t + Δ 2 u + a | u t | m ( ⋅ ) − 2 u t = [ u, F ( u ) ] + b | u | p ( ⋅ ) − 2 u where a and b are positive constants and the exponents m ( ⋅ ) and p ( ⋅ ) are given measurable functions. There are many literatures on the blow-up result of solutions for the wave equation. However, to the best of our knowledge, there is no blow-up result of solutions for von Karman equations. We investigate a finite time blow-up result of solutions with nonpositive initial energy as well as positive initial energy.