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We prove path-by-path uniqueness of solution to hyperbolic stochastic partialdifferential equations when the drift coefficient is the difference of twocomponentwise monotone Borel measurable functions of spatial linear growth. TheYamada-Watanabe principle for SDE driven by Brownian sheet then allows toderive strong uniqueness for such equation and thus extending the results in[Bogso, Dieye and Menoukeu Pamen, Elect. J. Probab., 27:1-26, 2022] and[Nualart and Tindel, Potential Anal., 7(3):661--680, 1997]. Assuming that thedrift is globally bounded, we show that the unique strong solution is Malliavindifferentiable. The case of spatial linear growth drift coefficient is alsostudied.

Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts