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

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