Long time behavior of small solutions in the viscous Klein–Gordon equation
Garénaux, Louis
1; Rijk, Björn de 1
1 Institut für Analysis (IANA), Karlsruher Institut für Technologie (KIT)
1; Rijk, Björn de 11 Institut für Analysis (IANA), Karlsruher Institut für Technologie (KIT)
Abstract:
For a viscous Klein-Gordon equation with quadratic nonlinearity, we prove that small solutions exist on exponentially long time scale. Our approach is based on the space-time resonance method in a diffusive setting. It allow to identify, through a simple computation, which of the non-linear effects are critical. The main technical challenge is to handle the interaction of two oscillating and diffusive modes.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsdatum | 06.02.2024 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000168325 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 21 S. |
| Serie | CRC 1173 Preprint ; 2024/4 |
| Projektinformation | SFB 1173/3 (DFG, DFG KOORD, SFB 1173/3) |
| Externe Relationen | Siehe auch |
| Schlagwörter | viscous Klein-Gordon equation, existence of small solutions, time reso- nances, temporal oscillations, quadratic non-linearity |
| Nachgewiesen in | arXiv |