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 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 is an element of R. This is different from the previous results, which proved the existence of exponentially decreasing solution only for t is an element of R+. As a consequence, we also construct exponentially decreasing solutions for time dependent PDE systems. (C) 2021 Published by Elsevier Inc.

Automated summary

This study examines the time-dependent hyperbolic system reduced from time-dependent PDE equations, and constructs exponentially decreasing solutions by carefully selecting initial datum. Unlike previous results, the solutions are found for the entire real number domain of time variable t, rather than just the positive real numbers.