Convergence in a quasilinear parabolic equation with Neumann boundary conditions
In: Nonlinear analysis, Jg. 74 (2011), Heft 4, S. 1426-1435
Online
academicJournal
- print, 12 ref
Consider the problem ut = a(ux)uxx + f(ux) (Ixl < 1, t > 0), ux(±1, t) = k±(t, u(±1, t)) (t > 0), where k± are smooth functions which are periodic in both t and u. Brunovský et al. proved in their paper (Brunovský et al., 1992 [8]) that if a time-global solution u is bounded then it converges to a periodic solution. We prove that if u is unbounded from above, then it converges to a periodic traveling wave V(x, t) + ct in case k± = k±(t) (or k± = k±(u)), where V is a time periodic function and c > 0. In addition, the periodic traveling wave is unique up to space shifts (or time shifts), it is stable and asymptotically stable. The average traveling speed c and the instantaneous speed Vt + c are also studied.
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Convergence in a quasilinear parabolic equation with Neumann boundary conditions
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Autor/in / Beteiligte Person: | JINGJING, CAI ; BENDONG, LOU |
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Zeitschrift: | Nonlinear analysis, Jg. 74 (2011), Heft 4, S. 1426-1435 |
Veröffentlichung: | Amsterdam: Elsevier, 2011 |
Medientyp: | academicJournal |
Umfang: | print, 12 ref |
ISSN: | 0362-546X (print) |
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