The existence of exponentially decreasing solutions to time dependent hyperbolic systems

We consider the time-dependent hyperbolic system which can be reduced from the time dependent PDE equations, such as the time-dependent complex Ginzburg-Landau equations, Boussinesq equations and sublinear Duffing equations, which are infinite-dimensional systems and finite-dimensional systems respe...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2021-09, Vol.501 (2), p.125199, Article 125199
Main Authors: Cheng, Hongyu, Xu, Lu
Format: Article
Language:English
Subjects:
Finite-dimensional systems
Hyperbolic systems
Infinite-dimensional systems
Initial datum
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Summary:We consider the time-dependent hyperbolic system which can be reduced from the time dependent PDE equations, such as the time-dependent complex Ginzburg-Landau equations, Boussinesq equations and sublinear Duffing equations, which are infinite-dimensional systems and finite-dimensional systems respectively. Note that the solution to the hyperbolic system is very sensitive to initial datum, by carefully choosing the initial datum, we construct some exponentially decreasing solution with respect to time-variable t∈R. This is different from the previous results, which proved the existence of exponentially decreasing solution only for t∈R+. As a consequence, we also construct exponentially decreasing solutions for time dependent PDE systems.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.125199