Abstract
We consider two-phase solutions to the Neumann initial-boundary value problem for the parabolic equation ut =[ϕ( u )] xx , where ϕ is a nonmonotone cubic-like function. First, we prove global existence for a restricted class of initial data _u_0, showing that two-phase solutions can be obtained as limiting points of the family of solutions to the Neumann initial-boundary value problem for the regularized equation _ut_ε = [ϕ(_u_ε)] xx + ε_utxx_ε (ε > 0). Then, assuming global existence, we study the long-time behaviour of two-phase solutions for any initial datum _u_0.
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 callMore From: Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications
Disclaimer: 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.
