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Global Existence and Decay of Small Solutions for Quasi-Linear Second-Order Uniformly Dissipative Hyperbolic-Hyperbolic Systems
This paper is concerned with quasilinear systems of partial differential equations consisting of two hyperbolic operators interacting dissipatively. Its main theorem establishes global-in-time existence and asymptotic stability of strong solutions to the Cauchy problem close to homogeneous reference states in d ≥ 3 space dimensions. Notably, the operators are not …