Publications [#347997] of Jian-Guo Liu

Papers Published

1. De Hoop, MV; Liu, JG; Markowich, PA; Ussembayev, NS, Plane-wave analysis of a hyperbolic system of equations with relaxation in ℝ^d, Communications in Mathematical Sciences, vol. 17 no. 1 (January, 2019), pp. 61-79 [doi] [high impact paper]
   (last updated on 2024/04/18)

   Abstract:
   We consider a multi-dimensional scalar wave equation with memory corresponding to the viscoelastic material described by a generalized Zener model. We deduce that this relaxation system is an example of a non-strictly hyperbolic system satisfying Majda's block structure condition. Wellposedness of the associated Cauchy problem is established by showing that the symbol of the spatial derivatives is uniformly diagonalizable with real eigenvalues. A long-time stability result is obtained by plane-wave analysis when the memory term allows for dissipation of energy.