Abstract
We study a quasilinear nonlocal Benney system and establish the existence and uniqueness of strong local in time solutions to the corresponding Cauchy problem. We also show, under certain conditions, the blow-up of such solutions in finite time. Furthermore, we prove the existence of global weak solutions and exhibit bound-state solutions to this system.
| Original language | English |
|---|---|
| Pages (from-to) | 135-156 |
| Number of pages | 22 |
| Journal | Journal of Hyperbolic Differential Equations |
| Volume | 14 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Mar 2017 |
Keywords
- Benney systems
- Blow-up
- Bound-state solutions
- Cauchy problem
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Dias, J. P., & Oliveira, F. (2017). On a quasilinear nonlocal Benney system. Journal of Hyperbolic Differential Equations, 14(1), 135-156. https://doi.org/10.1142/S0219891617500047