Well‐posedness and scattering of solutions to the sixth‐order Boussinesq type equation in the framework of modulation spaces

In this paper, we investigate the initial value problem for the sixth order Boussinesq type equation in the framework of modulation spaces. Under suitable conditions, we first prove that the problem has a unique local solutions and global solutions. Then scattering and stability of solutions are als...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-05, Vol.43 (8), p.5507-5521
Main Authors: Wang, Yu‐Zhu, Li, Weijia
Format: Article
Language:English
Subjects:
Boundary value problems
Boussinesq equations
global solutions
Mapping
Modulation
modulation spaces
Scattering
sixth‐order Boussinesq type equation
stability
Well posed problems
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Summary:In this paper, we investigate the initial value problem for the sixth order Boussinesq type equation in the framework of modulation spaces. Under suitable conditions, we first prove that the problem has a unique local solutions and global solutions. Then scattering and stability of solutions are also discussed. The proof is mainly based on the decay properties of the solutions operator in modulation spaces and the contraction mapping principle.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6291