Plane-wave analysis of a hyperbolic system of equations with relaxation in $mathbb{R}^{d}$


Abstract in English

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 Majdas block structure condition. Well-posedness 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.

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