Global smooth solutions for hyperbolic systems with time-dependent damping

被引:0
作者
Liu, Cunming [1 ]
Sheng, Han [1 ]
Lai, Ning-An [2 ]
机构
[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China
[2] Zhejiang Normal Univ, Sch Math Sci, Jinhua 321004, Zhejiang, Peoples R China
关键词
Hyperbolic system; Energy estimate; Stability condition; Smooth solution; COMPRESSIBLE EULER EQUATIONS; SINGULARITY FORMATION; ASYMPTOTIC-BEHAVIOR; WAVE-EQUATIONS; CAUCHY-PROBLEM; EXISTENCE; ENTROPY; BLOWUP;
D O I
10.1016/j.na.2024.113608
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The Cauchy problem for hyperbolic systems of balance laws admits global smooth solutions near the constant states under stability condition. This was widely studied in previous works. In this paper, we concern hyperbolic systems with time-dependent damping mu(1+t)(-lambda)G(U) with mu>0,lambda>0. In the following two cases, (i)lambda=1,mu>mu(0), where mu(0)>0 is a constant depending only on the coefficients of the system; (ii)0<lambda<1,mu>0, we prove that the smooth solutions exist globally when the initial data is small. To obtain these stability results, we establish uniform energy estimates and various dissipative estimates for all time and employ an induction argument on the order of derivatives of smooth solutions. Finally, we apply these results to some physical models.
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页数:22
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