Abstract
In this paper, we consider the following linear Korteweg–de Vries–Benjamin Bona Mahony (KdV-BBM) equation on a finite interval. { u u ut (0 (x,− , t 0)a ) 2 = =uxxt u u (0 L, (+x t )u ) ,x = + ux u (xxx L, t = ) = 0, 0, t (x, ∈ t (0 ) ∈ , ∞ (0 ) , L) × (0, ∞), x ∈ (0, L). We show the well-posedness by the semigroup theory. A set of critical length L is obtained, for which the system possesses conservative solutions. Then we prove the exponentially stability of the associated semigroup when L ∉ L by the frequency domain method.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1206-1216 |
| Number of pages | 11 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 29 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 2024 |
Bibliographical note
Publisher Copyright:© 2024 American Institute of Mathematical Sciences. All rights reserved.
Keywords
- Exponential Stability
- KdV-BBM equation
- Well-posedness