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math.AP2017
Existence and nonexistence theorems for global weak solutions to quasilinear wave equations for the elasticity
Yun-guang Lu, Yuusuke Sugiyama
In this paper, by using the theory of compensated compactness coupled with the kinetic formulation by Lions, Perthame, Souganidis and Tadmor \cite{LPT,LPS}, we prove the existence…
math.AP2017
Singularity formation for the 1D compressible Euler equation with variable damping coefficient
Yuusuke Sugiyama
In this paper, we consider some blow-up problems for the 1D Euler equation with time and space dependent damping. We investigate sufficient conditions on initial data and the rate…