Existence and nonexistence theorems for global weak solutions to quasilinear wave equations for the elasticity
Existence and nonexistence theorems for global weak solutions to quasilinear wave equations for the elasticity
复制标题
弹性拟线性波动方程全局弱解的存在与不存在定理
DOI：
10.1016/j.aml.2018.05.001
复制
发表时间：
2018
影响因子：
3.7
通讯作者：
杉山裕介
中科院分区：
文献类型：
--
作者：
Yunguang Lu;杉山裕介
本文证明了具有非负初值v0(X)和S>；1的非线性退化波动方程vt=c(|v|S−1 v)x x整体广义(非负)解的存在性和不存在性。这些结果推广了第二作者的结果(Sugiyama，2016)，在初值为∫−∞∞v1(X)dx和非退化条件v0(X)≥c0>；0的条件下，研究了唯一的整体经典解的存在性和不存在性。
We prove the existence and nonexistence of global generalized (nonnegative) solutions of the nonlinearly degenerate wave equations v t t= c (| v| s− 1 v) x x with the nonnegative initial data v 0 (x) and s> 1. These results are extensions of the results in the second author’s paper (Sugiyama, 2016), where the existence and the nonexistence of the unique global classical solution were studied with a threshold on∫−∞∞ v 1 (x) d x and the non-degeneracy condition v 0 (x)≥ c 0> 0 on the initial data.