Abstract
We study traveling waves bifurcating from stable standing layers in systems where a reaction-diffusion equation couples to a scalar conservation law. We prove the existence of weekly decaying traveling fronts that emerge in the presence of a weakly stable direction on a center manifold. Moreover, we show the existence of bifurcating traveling waves of constant mass. The main difficulty is to prove the smoothness of the ansatz in exponentially weighted spaces required to apply the Lyapunov-Schmidt methods.
Original language | English (US) |
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Pages (from-to) | 2619-2651 |
Number of pages | 33 |
Journal | Discrete and Continuous Dynamical Systems- Series A |
Volume | 37 |
Issue number | 5 |
DOIs | |
State | Published - May 2017 |
Keywords
- Bifurcation
- Conservation law
- Far-field corrections
- Lyapunov-Schmidt reduction
- Traveling waves