Abstract
This paper is concerned with blow-up phenomena and global existence for the periodic two-component Dullin-Gottwald-Holm system. We first obtain several blow-up results and the blow-up rate of strong solutions to the system. We then present a global existence result for strong solutions to the system. MSC: 35G25; 35L05
Highlights
In this paper, we consider the following periodic two-component Dullin-Gottwald-Holm (DGH) system: ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨umρt(t +, x(Au) ρu=)xux+ =(ux m), x+ uxm t >, x x ∈ R, + ∈ γ uxxx R, + ρρx =⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩ρρu(((t t,xxx+)+= ))ρ== (uρx()(t,t, x x), x), ∈
The aim of this paper is to further study the blow-up phenomena for strong solutions to ( . ) and to present a global existence result
In Section, we present a new global existence result of strong solutions to ( . )
Summary
In Section , we present a new global existence result of strong solutions to [ ] Given the initial data (u , ρ ) ∈ Hs × Hs– , s ≥ , there exists a maximal T = T( (u , ρ ) Hs×Hs– ) > and a unique solution (u, ρ) ∈ C [ , T); Hs × Hs– ∩ C [ , T); Hs– × Hs–
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
