Global well‐posedness for strongly damped multidimensional generalized Boussinesq equations. (22nd February 2016)

• Record Type: Journal Article
• Authors: Jihong, Shen; Mingyou, Zhang; Xingchang, Wang; Bowei, Liu; Runzhang, Xu
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 15(2016:Oct. 15)
• Page Start: 4437
• Page End: 4450
• Publication Date: 2016-02-22
• Subjects: stong damping -- Boussinesq equations -- Cauchy problem -- global existence -- nonexistence -- potential well method; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3873
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We study the Cauchy problem for a class of strongly damped multidimensional generalized Boussinesq equations u t t −Δ u −Δ u t t +Δ 2 u +Δ 2 u t t − k Δ u t =Δ f ( u ), where k is a positive constant. Under some assumptions and by using potential well method, we prove the existence and nonexistence of global weak solution without solution without establishing the local existence theory. Copyright © 2016 John Wiley & Sons, Ltd.