Premium
Global well‐posedness and scattering of a generalized nonlinear fourth‐order wave equation
Author(s) -
Gao Chuanwei,
Lu Jing
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4352
Subject(s) - mathematics , compact space , scattering , cauchy problem , mathematical analysis , wave equation , scattering theory , nonlinear system , order (exchange) , momentum (technical analysis) , initial value problem , physics , quantum mechanics , finance , economics
In this paper, we study the global well‐posedness and scattering theory of the solution to the Cauchy problem of a generalized fourth‐order wave equation∂ t t u +Δ2 u − Δ u + u = − | u | p − 1 u ,u ( 0 , x ) = u 0 ( x ) ∈ H 2 ( R d ) ,u t ( 0 , x ) = u 1 ( x ) ∈ L 2 ( R d ) ,where 1 + 4 d < p < 2 ∗ , 2 ∗ = ∞ if d ⩽4, and2 ∗ = d + 4 d − 4if d ⩾5. The main strategy we use in this paper is concentration‐compactness argument, which was first introduced by Kenig and Merle to handle the scattering problem vector so as to control the momentum. Copyright © 2017 John Wiley & Sons, Ltd.