Plane-wave analysis of a hyperbolic system of equations with relaxation in R^d
Type
ArticleKAUST Department
Applied Mathematics and Computational ScienceApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2019Permanent link to this record
http://hdl.handle.net/10754/655965
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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.Citation
De Hoop, M. V., Liu, J.-G., Markowich, P. A., & Ussembayev, N. S. (2019). Plane-wave analysis of a hyperbolic system of equations with relaxation in $\mathbb{R}^d$. Communications in Mathematical Sciences, 17(1), 61–79. doi:10.4310/cms.2019.v17.n1.a3Sponsors
M.V.d.H. gratefully acknowledges support from the Simons Foundation under the MATH + X program, the National Science Foundation under grant DMS-1559587, and the corporate members of the GeoMathematical Group at Rice University. J.-G.L. is supported by the National Science Foundation under grant DMS-1812573 and KI-Net RNMS11-07444.Publisher
International Press of Bostonae974a485f413a2113503eed53cd6c53
10.4310/cms.2019.v17.n1.a3