First and second order approximations for a nonlinear wave equation. (English) Zbl 1270.65060
The author discusses the first- and second-order approximations for a nonlinear wave equation. She first explains the need of splitting the nonlinearity into its resonant and oscillatory part, which is the ground for both the renormalization group (RG) and the averaging method. Later, the author presents the RG method and uses it to prove some theorems. For a better understanding of the second-order approximation, she proves a theorem from a paper of P. Gérard and S. Grellier [Anal. PDE 5, No. 5, 1139–1155 (2012; Zbl 1268.35013)] using the RG method. In addition, the author presents an averaging method of the second order and uses it to prove an additional theorem.
Reviewer: Seenith Sivasundaram (Daytona Beach)
MSC:
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35Q35 | PDEs in connection with fluid mechanics |
| 35L70 | Second-order nonlinear hyperbolic equations |
Citations:
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