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arXiv · 2306.09653

Temporal periodic solutions to nonhomogeneous quasilinear hyperbolic equations driven by time-periodic boundary conditions

Xixi Fang·Peng Qu·Huimin Yu
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Abstract

We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness of the time-periodic classical solutions are obtained.Moreover, the W2, regularity and stability around the time-periodic solutions are discussed. Our results reveal that the feedback boundary control with dissipative structure can stabilize the K-weakly diagonally dominant nonhomogeneous quasilinear hyperbolic system around the temporal periodic solution.

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Xixi Fang, Peng Qu, Huimin Yu. 2023-06-16. Temporal periodic solutions to nonhomogeneous quasilinear hyperbolic equations driven by time-periodic boundary conditions. https://arxiv.org/abs/2306.09653

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