Abstract
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.
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The authors are partially supported by the Outstanding Youth Fund of Zhejiang Province (Grant No. LR22A010004), the NSFC (Grant No. 12071435).
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Jiang, Q., Wei, C. & Xing, T. The Global Classical Solution and Asymptotic Behavior of the Cauchy Problem for Hyperbolic Monge-Ampère Equation. Results Math 79, 12 (2024). https://doi.org/10.1007/s00025-023-02028-9
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DOI: https://doi.org/10.1007/s00025-023-02028-9