Research of global behavior of classical solutions for quasilinear Wave equations

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In this study, we succeeded in the classification of the sufficient conditions (null-conditions) for the global existence of the classical solutions to the system of nonlinear wave equations in 2 and 3 space dimensions, according to the type of the nonlinear terms (Null-form type, Non-resonance type and Nonlinear dissipation type). As development of the research, we also obtained precise evaluations to the lifespan of the classical solutions for the first order hyperbolic PDE systems with multiple propagation speeds and for the nonlinear elastic wave equations.