The Global Classical Solution and Asymptotic Behavior of the Cauchy Problem for Hyperbolic Monge-Ampère Equation

This paper is concerned with the hyperbolic partial differential equations of Monge-Ampère type with two independent variables. When the coefficients do not depend on the unknown function and its derivatives, we can show that the hyperbolic Monge-Ampère equation admits a global classical solution by the energy method under some decay and smallness assumptions on the coefficients. Furthermore, we can show that the solution converges to a solution of the linearized system.