We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third ord...We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.展开更多
基金partially supported by the National Nature Science Foundation of China(12271114)the Guangxi Natural Science Foundation(2023JJD110009,2019JJG110003,2019AC20214)+2 种基金the Innovation Project of Guangxi Graduate Education(JGY2023061)the Key Laboratory of Mathematical Model and Application(Guangxi Normal University)the Education Department of Guangxi Zhuang Autonomous Region。
文摘We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.
