Abstract
We consider the semilinear parabolic equation ut = uxx + f(u) on the real line, where f is a locally Lipschitz function on R. We prove that if a solution u of this equation is bounded and its initial value u(x, 0) has distinct limits at x = ±∞ , then the solution is quasiconvergent, that is, all its limit profles as t → ∞ are steady states.
Original language | English (US) |
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Pages (from-to) | 4423-4441 |
Number of pages | 19 |
Journal | Nonlinearity |
Volume | 31 |
Issue number | 9 |
DOIs | |
State | Published - Aug 7 2018 |
Bibliographical note
Publisher Copyright:© 2018 IOP Publishing Ltd & London Mathematical Society Printed in the UK.
Keywords
- Parabolic equations on the real line
- convergence
- convergent initial data
- quasiconvergence